:分别用伴随矩阵法和初等变换法-|||-求矩阵 (1/3 2/4) 的逆矩阵?
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A =
[1 2]
[3 4]
伴随矩阵法求矩阵 : |A| = -2
A* =
[ 4 -2]
[-3 1]
A^(-1) = A*/|A| =
[ -2 1]
[3/2 -1/2]
初等变换法求矩阵 :
(A, E) =
[1 2 1 0]
[3 4 0 1]
初等行变换为
[1 2 1 0]
[0 -2 =3 1]
初等行变换为
[1 0 -2 1]
[0 -2 =3 1]
初等行变换为
[1 0 -2 1]
[0 1 3/2 -1/2]
A^(-1) =
[ -2 1]
[3/2 -1/2]
[1 2]
[3 4]
伴随矩阵法求矩阵 : |A| = -2
A* =
[ 4 -2]
[-3 1]
A^(-1) = A*/|A| =
[ -2 1]
[3/2 -1/2]
初等变换法求矩阵 :
(A, E) =
[1 2 1 0]
[3 4 0 1]
初等行变换为
[1 2 1 0]
[0 -2 =3 1]
初等行变换为
[1 0 -2 1]
[0 -2 =3 1]
初等行变换为
[1 0 -2 1]
[0 1 3/2 -1/2]
A^(-1) =
[ -2 1]
[3/2 -1/2]
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