a92364ac-8053-461f-addc-9a15196425a4 3 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

n M i 1 n range j 1 n range M i j el i j * : for for M 21 line :

The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in its row echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.

rows/cols are NOT linearly independent 9 M rank 1

9 M det 0

M 1212 - 3 - 135033 mat :

M rank 2

Q 7 - 232110721 - 1 - 3 - 34 mat :

N 11021 - 1 - 02 - 24 mat :

N rank 1

Q rank 2

U 0111 - 000001001 - 10001 - 110000055 mat :

U det 0

U U 14 range 25 range el :

U rank 3

U det 0

U 111 - 0000101 - 1001 - 1144 mat