矩阵化简。。
2个回答
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AX = 2E, X = 2A^(-1)
(A, E) =
[ 1 2 -1 1 0 0]
[ 1 6 -2 0 1 0]
[-1 2 1 0 0 1]
初等行变换为
[ 1 2 -1 1 0 0]
[ 0 4 -1 -1 1 0]
[ 0 4 0 1 0 1]
初等行变换为
[ 1 0 -1 1/2 0 -1/2]
[ 0 1 0 1/4 0 1/4]
[ 0 0 -1 -2 1 -1]
初等行变换为
[ 1 0 0 5/2 -1 1/2]
[ 0 1 0 1/4 0 1/4]
[ 0 0 1 2 -1 1]
A^(-1) =
[5/2 -1 1/2]
[1/4 0 1/4]
[ 2 -1 1]
X = 2A^(-1) =
[ 5 -1 1]
[1/2 0 1/2]
[ 4 -2 2]
(A, E) =
[ 1 2 -1 1 0 0]
[ 1 6 -2 0 1 0]
[-1 2 1 0 0 1]
初等行变换为
[ 1 2 -1 1 0 0]
[ 0 4 -1 -1 1 0]
[ 0 4 0 1 0 1]
初等行变换为
[ 1 0 -1 1/2 0 -1/2]
[ 0 1 0 1/4 0 1/4]
[ 0 0 -1 -2 1 -1]
初等行变换为
[ 1 0 0 5/2 -1 1/2]
[ 0 1 0 1/4 0 1/4]
[ 0 0 1 2 -1 1]
A^(-1) =
[5/2 -1 1/2]
[1/4 0 1/4]
[ 2 -1 1]
X = 2A^(-1) =
[ 5 -1 1]
[1/2 0 1/2]
[ 4 -2 2]
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