作业帮线性代数麻烦解题
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线性代数麻烦解题
线性代数麻烦解题
线性代数麻烦解题
知识点:A* = |A|A^-1 (A可逆时)
|A*| = |A|^(n-1)
(kA)^-1 = (1/k)A^-1
|A^-1| = 1/|A|
|kA| = k^n|A|
|A*| = |A|^2 = 4.
A* = |A|A^-1 = 2A^-1
|((-1/2)A)^-1 - 2A*| = | -2A^-1 - 4A^-1| = |-6A^-1| = (-6)^3 (1/|A|) = - 6^3/2 = -108.
|2A*B^-1| = 2^3|A*||B^-1| = 8 * |A|^2 * |B|^-1 = 8*2^2 /3 = 32/3
不麻烦的，根据伴随矩阵的公式AA*=|A|E,得到当矩阵可逆的时候A*=|A|A^(-1)
代入得第一个式子=|-2A^(-1)-2|A|A^(-1)|=|-6A^(-1)|=-108
代入第二个式子=|2|A|A^(-1)B^(-1)|=|4A^(-1)B^(-1)|=32/3
A* = |A|A^-1 (A可逆时)
|A*| = |A|^(n-1)
(kA)^-1 = (1/k)A^-1
|A^-1| = 1/|A|
|kA| = k^n|A|
解答: |A*| = |A|^2 = 4.
A* = |A|A^-1 =...
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A* = |A|A^-1 (A可逆时)
|A*| = |A|^(n-1)
(kA)^-1 = (1/k)A^-1
|A^-1| = 1/|A|
|kA| = k^n|A|
解答: |A*| = |A|^2 = 4.
A* = |A|A^-1 = 2A^-1
|((-1/2)A)^-1 - 2A*| = | -2A^-1 - 4A^-1| = |-6A^-1| = (-6)^3 (1/|A|) = - 6^3/2 = -108.
|2A*B^-1| = 2^3|A*||B^-1| = 8 * |A|^2 * |B|^-1 = 8*2^2 /3 = 32/3
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