Question

reduse the matrix in the normal form and find its rank and nutility A=[3, 5,7,2,3,4,1,2,3]​

Answer 1

We first obtain the reduced row echelon form matrix corresponding to the matrix A.

We reduce the matrix A as follows:

A=[ 2 4 6 8 1 3 0 5 1 1 6 3 ]

1

2

R1

→

[ 1 2 3 4 1 3 0 5 1 1 6 3 ]

R2−R1

→

R3−R1

[ 1 2 3 4 0 1 −3 1 0 −1 3 −1 ]

R1−2R2

→

R3+R2

[ 1 0 9 2 0 1 −3 1 0 0 0 0 ].

The last matrix is in reduced row echelon form. That is,

rref(A)=[ 1 0 9 2 0 1 −3 1 0 0 0 0 ].