Question

用初等变换的方法求解矩阵方程AX=B

Answer 1

(A,B) =

[ 1 3 8 -3 5]

[ 2 4 11 1 5]

[ 1 2 5 3 4]

行初等变换为

[ 1 3 8 -3 5]

[ 0 -2 -5 7 -5]

[ 0 -1 -3 6 -1]

行初等变换为

[ 1 0 -1 15 2]

[ 0 1 3 -6 1]

[ 0 0 1 -5 -3]

行初等变换为

[ 1 0 0 10 -1]

[ 0 1 0 9 10]

[ 0 0 1 -5 -3]

得 X =

[10 -1]

[ 9 10]

[-5 -3]