线性代数问题
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17 . AX = A+X, (A-E)X = A, X = (A-E)^(-1)A.
(A-E, A) =
[0 2 1 1 2 1]
[3 3 2 3 4 2]
[1 2 1 1 2 2]
初等行变换为
[1 2 1 1 2 2]
[0 2 1 1 2 1]
[0 -3 -1 0 -2 -4]
初等行变换为
[1 0 0 0 0 1]
[0 2 1 1 2 1]
[0 0 1/2 3/2 1 -5/2]
初等行变换为
[1 0 0 0 0 1]
[0 2 0 -2 0 6]
[0 0 1 3 2 -5]
初等行变换为
[1 0 0 0 0 1]
[0 1 0 -1 0 3]
[0 0 1 3 2 -5]
X = (A-E)^(-1)A =
[ 0 0 1]
[-1 0 3]
[ 3 2 -5]
18. (A, E) =
[ 3 0 8 1 0 0]
[ 3 -1 6 0 1 0]
[-2 0 -5 0 0 1]
初等行变换为
[ 3 0 8 1 0 0]
[ 0 -1 -2 -1 1 0]
[ 0 0 1/3 2/3 0 1]
初等行变换为
[ 3 0 0 -15 0 -24]
[ 0 -1 0 3 1 6]
[ 0 0 1 2 0 3]
初等行变换为
[ 1 0 0 -5 0 -8]
[ 0 1 0 -3 -1 -6]
[ 0 0 1 2 0 3]
A^(-1) =
[-5 0 -8]
[-3 -1 -6]
[ 2 0 3]
(A-E, A) =
[0 2 1 1 2 1]
[3 3 2 3 4 2]
[1 2 1 1 2 2]
初等行变换为
[1 2 1 1 2 2]
[0 2 1 1 2 1]
[0 -3 -1 0 -2 -4]
初等行变换为
[1 0 0 0 0 1]
[0 2 1 1 2 1]
[0 0 1/2 3/2 1 -5/2]
初等行变换为
[1 0 0 0 0 1]
[0 2 0 -2 0 6]
[0 0 1 3 2 -5]
初等行变换为
[1 0 0 0 0 1]
[0 1 0 -1 0 3]
[0 0 1 3 2 -5]
X = (A-E)^(-1)A =
[ 0 0 1]
[-1 0 3]
[ 3 2 -5]
18. (A, E) =
[ 3 0 8 1 0 0]
[ 3 -1 6 0 1 0]
[-2 0 -5 0 0 1]
初等行变换为
[ 3 0 8 1 0 0]
[ 0 -1 -2 -1 1 0]
[ 0 0 1/3 2/3 0 1]
初等行变换为
[ 3 0 0 -15 0 -24]
[ 0 -1 0 3 1 6]
[ 0 0 1 2 0 3]
初等行变换为
[ 1 0 0 -5 0 -8]
[ 0 1 0 -3 -1 -6]
[ 0 0 1 2 0 3]
A^(-1) =
[-5 0 -8]
[-3 -1 -6]
[ 2 0 3]
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