Question

线性代数,将这个矩阵化为最简形

Answer 1

A=

[1 2 3 4 -4]

[0 1 -1 1 2]

[1 3 0 3 -1]

[0 -2 1 1 2]

行初等变换为

[1 2 3 4 -4]

[0 1 -1 1 2]

[0 1 -3 -1 3]

[0 -2 1 1 2]

行初等变换为

[1 0 5 2 -8]

[0 1 -1 1 2]

[0 0 -2 -2 1]

[0 0 -1 3 6]

行初等变换为

[1 0 0 17 22]

[0 1 0 -2 -4]

[0 0 1 -3 -6]

[0 0 0 -8 -11]

行初等变换为

[1 0 0 0 -11/8]

[0 1 0 0 -5/4]

[0 0 1 0 -15/8]

[0 0 0 1 11/8]