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  <settings>
    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>60</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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  <region id="0" left="18" top="18" width="324" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Beispiel: Auflagerreaktionen berechnen</p>
    </text>
    <text lang="eng">
      <p bold="true">Example: Compute Support Reactions</p>
    </text>
  </region>
  <region id="1" left="522" top="18" width="169" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section linsolve.sm">Lineare Gleichungen</p>
    </text>
    <text lang="eng">
      <p href="Section linsolve.sm">Solving Linear Equations</p>
    </text>
  </region>
  <region id="2" left="522" top="36" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="3" left="522" top="54" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="4" left="18" top="90" width="562" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Zu bestimmen sind die Auflagerreaktionen für das skizzierte System.</p>
    </text>
    <text lang="eng">
      <p>Determine the support reactions for the given system</p>
    </text>
  </region>
  <region id="5" left="18" top="126" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gegeben:</p>
    </text>
    <text lang="eng">
      <p>Given:</p>
    </text>
  </region>
  <region id="6" left="108" top="126" width="66" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F</e>
        <e type="operand">1</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="189" top="126" width="54" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand" preserve="false" style="unit">a.0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="8" left="261" top="126" width="66" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">a.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="18" top="162" width="118" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gesucht: A, B</p>
    </text>
    <text lang="eng">
      <p>Unknown: A, B</p>
    </text>
  </region>
  <region id="10" left="18" top="189" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Freischnitt:</p>
    </text>
    <text lang="eng">
      <p>Free body diagram</p>
    </text>
  </region>
  <region id="11" left="18" top="207" width="505" height="136" color="#000000" bgColor="#ffffff">
    <picture readOnly="false">
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="12" left="18" top="351" width="547" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Lösung mit dem allgemeinen Verfahren für nichtlineare Gleichungen</p>
    </text>
    <text lang="eng">
      <p underline="true">Solution using the general non-linear procedure</p>
    </text>
  </region>
  <region id="13" left="18" top="387" width="259" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Kräftegleichgewicht senkrecht:</p>
    </text>
    <text lang="eng">
      <p>Vertical force equillibrium</p>
    </text>
  </region>
  <region id="14" left="270" top="387" width="115" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">Gl</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operator" args="2">+</e>
        <e type="operand">F</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="15" left="450" top="387" width="291" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Gleichungen müssen in Klammern
stehen, da der Operator = höhere 
Priorität als der Zuweisungs-
operator hat.</p>
    </text>
    <text lang="eng">
      <p>Equations must be in brackets due
to the low priority of the 
boolean equal operator.</p>
    </text>
  </region>
  <region id="16" left="18" top="423" width="209" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Momentengleichgewicht um
Punkt A</p>
    </text>
    <text lang="eng">
      <p>Moment equillibrium about A</p>
    </text>
  </region>
  <region id="17" left="270" top="423" width="153" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">Gl</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">B</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="18" left="18" top="468" width="649" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Mit der Funktion Unknowns() kann man prüfen, ob tatsächlich nur die gesuchten 
Größen unbekannt sind:</p>
    </text>
    <text lang="eng">
      <p>The function Unknowns() checks the given system of equations for any undefined 
variables. These should match the unknowns that you want to solve for.</p>
    </text>
  </region>
  <region id="19" left="18" top="513" width="148" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="function" preserve="true" args="1">Unknowns</e>
      </input>
      <result action="symbolic">
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="20" left="207" top="522" width="222" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>(symbolisch auswerten mit </p>
    </text>
    <text lang="eng">
      <p>(evaluate symbolically using</p>
    </text>
  </region>
  <region id="21" left="459" top="522" width="61" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Strg+.</p>
    </text>
    <text lang="eng">
      <p>Ctrl+.</p>
    </text>
  </region>
  <region id="22" left="513" top="522" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>)</p>
    </text>
  </region>
  <region id="23" left="18" top="558" width="718" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Wir haben also zwei Gleichungen  und zwei Unbekannte. Den Unbekanntenvektor
kopieren wir in die Parameterliste von FindRoot() und ergänzen die Startwerte so, dass
die physikalische Dimension passt, hier sind Kräfte gesucht, also sind die Startwerte
Kräfte.</p>
    </text>
    <text lang="eng">
      <p>Thus we have two equations and two unknowns. The vector of unknowns is copied to the
parameter list of FindRoot() and initial values of matching physical dimension are
added. In the given case the unknowns are forces, thus their initial values are 
forces as well.</p>
    </text>
  </region>
  <region id="24" left="18" top="630" width="266" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">A</e>
        <e type="operand">F</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">B</e>
        <e type="operand">F</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">0.3333</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="25" left="297" top="648" width="117" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="26" left="441" top="648" width="117" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
      </input>
      <result action="numeric">
        <e type="operand">0.3333</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="27" left="18" top="702" width="718" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Wie man rechts sieht, wurden die Variablen bereits mit der Lösung belegt. Dies ist ein
sehr angenehmes Merkmal der Funktion FindRoot()</p>
    </text>
    <text lang="eng">
      <p>As you can see, the variables were assigned the found values. This is a very 
convenient feature of the function FindRoot().</p>
    </text>
  </region>
  <region id="28" left="18" top="756" width="389" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Lösung mit der Funktion LinSolve aus dem Maxima-Plugin</p>
    </text>
    <text lang="eng">
      <p underline="true">Solution using LinSolve from the Maxima plugin</p>
    </text>
  </region>
  <region id="29" left="18" top="792" width="636" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Das Verfahren funktioniert auch rein symbolisch, also muss keine der beteiligten
Variablen einen Wert haben:</p>
    </text>
    <text lang="eng">
      <p>This procedure can produce symbolic results. All variables may be undefined.</p>
    </text>
  </region>
  <region id="30" left="270" top="819" width="202" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">F</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="5">Clear</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="31" left="18" top="855" width="148" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gleichungssystem </p>
    </text>
    <text lang="eng">
      <p>System of equations</p>
    </text>
  </region>
  <region id="32" left="207" top="855" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Unbekannte </p>
    </text>
    <text lang="eng">
      <p>Unknowns </p>
    </text>
  </region>
  <region id="33" left="360" top="855" width="65" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Lösung </p>
    </text>
    <text lang="eng">
      <p>Solution</p>
    </text>
  </region>
  <region id="34" left="18" top="882" width="158" height="52" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
      </input>
      <result action="symbolic">
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">F</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">B</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="35" left="207" top="882" width="148" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="function" preserve="true" args="1">Unknowns</e>
      </input>
      <result action="symbolic">
        <e type="operand">a</e>
        <e type="operand">A</e>
        <e type="operand">b</e>
        <e type="operand">B</e>
        <e type="operand">F</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="36" left="360" top="882" width="244" height="84" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">LinSolve</e>
      </input>
      <result action="symbolic">
        <e type="operand">A</e>
        <e type="operand">b</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operand">B</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">mat</e>
      </result>
    </math>
  </region>
  <region id="37" left="18" top="981" width="491" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Wie man sieht, sind keine Startwerte erforderlich, es gibt 
aber auch keine eingebettete Ergebniszuweisung.</p>
    </text>
    <text lang="eng">
      <p>As can be seen, there are no initial values required. However, there is no
embedded results assignment.</p>
    </text>
  </region>
  <region id="38" left="18" top="1026" width="522" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Man kann aber die Funktion Assign() für die Zuweisung benutzen</p>
    </text>
  </region>
  <region id="39" left="18" top="1053" width="276" height="80" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">LinSolve</e>
        <e type="function" preserve="true" args="1">Assign</e>
      </input>
      <result action="symbolic">
        <e type="operand">b</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">mat</e>
      </result>
    </math>
  </region>
  <region id="40" left="342" top="1071" width="78" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
      <result action="symbolic">
        <e type="operand">b</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
  <region id="41" left="486" top="1071" width="78" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
      </input>
      <result action="symbolic">
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
  <region id="42" left="18" top="1143" width="357" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Nun werden die gegebenen Daten eingesetzt:</p>
    </text>
  </region>
  <region id="43" left="18" top="1170" width="66" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F</e>
        <e type="operand">1</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="44" left="99" top="1170" width="54" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand" preserve="false" style="unit">a.0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="45" left="171" top="1170" width="66" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">a.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="46" left="270" top="1170" width="117" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="47" left="414" top="1170" width="117" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
      </input>
      <result action="numeric">
        <e type="operand">0.3333</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="48" left="18" top="1215" width="234" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Lösung mit Matrizenrechnung</p>
    </text>
    <text lang="eng">
      <p underline="true">Solution using matrix inversion</p>
    </text>
  </region>
  <region id="49" left="18" top="1251" width="357" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Das Gleichungssystem in Matrixform lautet:</p>
    </text>
    <text lang="eng">
      <p>System in matrix format</p>
    </text>
  </region>
  <region id="50" left="18" top="1287" width="135" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operator" args="2">*</e>
        <e type="operand">F</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="51" left="18" top="1341" width="407" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Dies wird nach dem Unbekanntenvektor umgestellt:</p>
    </text>
    <text lang="eng">
      <p>Solve for the vector of unknowns</p>
    </text>
  </region>
  <region id="52" left="18" top="1359" width="149" height="53" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">F</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="53" left="18" top="1413" width="570" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Lösung muss bei Bedarf noch auf die Variablen zugewiesen werden:</p>
    </text>
    <text lang="eng">
      <p>If required, the solution has to be assigned to the variables.</p>
    </text>
  </region>
  <region id="54" left="27" top="1440" width="57" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="55" left="108" top="1440" width="117" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="56" left="243" top="1440" width="57" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="57" left="315" top="1440" width="117" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
      </input>
      <result action="numeric">
        <e type="operand">0.3333</e>
        <e type="operand" preserve="false" style="unit">F.0</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="58" left="18" top="1485" width="665" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Das Matrizenverfahren funktioniert auch rein symbolisch ohne vorherige Belegung 
mit Werten:</p>
    </text>
    <text lang="eng">
      <p>The matrix approach also provides symbolic solutions with all variables undefined. </p>
    </text>
  </region>
  <region id="59" left="18" top="1521" width="202" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">F</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="5">Clear</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="60" left="18" top="1548" width="193" height="78" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">F</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="symbolic">
        <e type="operand">F</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">a</e>
        <e type="operand">F</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="61" left="18" top="1647" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="62" left="18" top="1665" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="63" left="18" top="1701" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-10-10 03:03:39 +0200 (Do, 10. Okt 2013) $ </p>
    </text>
  </region>
</regions>