Question

画三角的两个题 求解答 详细一点儿 谢谢啊

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Answer 1

24 用分块矩阵求逆方法。 B =
[5 2]
[2 1]
|B| = 1, B^(-1) = B*/|B| =
[ 1 -2]
[-2 1]
C =
[1 -2]
[1 1]
|C| = 3, C^(-1) = C*/|C| = (1/3)*
[ 1 2]
[-1 1]
则 A^(-1) =
[1 -2 0 0]
[-2 5 0 0]
[ 0 0 1/3 2/3]
[ 0 0 -1/3 1/3]

19(2) (A, E) =
[2 2 -1 1 0 0]
[1 -2 4 0 1 0]
[5 8 2 0 0 1]
初等行变换为
[1 -2 4 0 1 0]
[0 6 -9 1 -2 0]
[0 18 -18 0 -5 1]
初等行变换为
[1 -2 4 0 1 0]
[0 6 -9 1 -2 0]
[0 0 9 -3 1 1]
初等行变换为
[1 -2 0 4/3 5/9 -4/9]
[0 6 0 -2 -1 1]
[0 0 1 -1/3 1/9 1/9]
初等行变换为
[1 0 0 2/3 2/9 -1/9]
[0 1 0 -1/3 -1/6 1/6]
[0 0 1 -1/3 1/9 1/9]
A^(-1) =
[ 2/3 2/9 -1/9]
[-1/3 -1/6 1/6]
[-1/3 1/9 1/9]