Question

线性代数 求矩阵初等变换化为行最简行形

0 -2 1 1 0 0
3 0 -2 0 1 0
-2 3 0 0 01

Answer 1

[ 0 -2 1 1 0 0]
[ 3 0 -2 0 1 0]
[-2 3 0 0 0 1]
行初等变换为
[ 6 0 -4 0 2 0]
[ 0 -2 1 1 0 0]
[-6 9 0 0 0 3]
行初等变换为
[ 6 0 -4 0 2 0]
[ 0 -2 1 1 0 0]
[ 0 9 -4 0 2 3]
行初等变换为
[ 1 0 -2/3 0 1/3 0]
[ 0 1 -1/2 -1/2 0 0]
[ 0 9 -4 0 2 3]
行初等变换为
[ 1 0 -2/3 0 1/3 0]
[ 0 1 -1/2 -1/2 0 0]
[ 0 0 1/2 9/2 2 3]
行初等变换为
[ 1 0 0 6 3 8]
[ 0 1 0 4 2 3]
[ 0 0 1 2 4 6]