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6 (A, E) =
[ 1 0 -2 1 0 0]
[-3 1 4 0 1 0]
[ 2 -3 4 0 0 1]
初等行变换为
[ 1 0 -2 1 0 0]
[ 0 1 -2 3 1 0]
[ 0 -3 8 -2 0 1]
初等行变换为
[ 1 0 -2 1 0 0]
[ 0 1 -2 3 1 0]
[ 0 0 2 7 3 1]
初等行变换为
[ 1 0 0 8 3 1]
[ 0 1 0 10 4 1]
[ 0 0 2 7 3 1]
初等行变换为
[ 1 0 0 8 3 1]
[ 0 1 0 10 4 1]
[ 0 0 1 7/2 3/2 1/2]
A^(-1) =
[ 8 3 1]
[ 10 4 1]
[7/2 3/2 1/2]
7. 增广矩阵 (A, b) =
[ 1 3 -1 1 2]
[ 2 -1 1 -1 3]
[-1 -2 0 4 1]
初等行变换为
[ 1 3 -1 1 2]
[ 0 -7 3 -3 -1]
[ 0 1 -1 5 3]
初等行变换为
[ 1 0 2 -14 -7]
[ 0 1 -1 5 3]
[ 0 0 -4 32 20]
初等行变换为
[ 1 0 0 2 3]
[ 0 1 0 -3 -2]
[ 0 0 1 -8 -5]
初等行变换为
方程组化为
x1 = 3-2x4
x2 = -2+3x4
x3 = -5+8x4
取 x4 = 0, 得特解 (3, -2, -5, 0)^T;
导出组即
x1 = -2x4
x2 = 3x4
x3 = 8x4
取 x4 = 1, 得Ax = 0 的基础解系 (-2, 3, 8, 1)^T
方程组的通解是 x = k(-2, 3, 8, 1)^T + (3, -2, -5, 0)^T。
[ 1 0 -2 1 0 0]
[-3 1 4 0 1 0]
[ 2 -3 4 0 0 1]
初等行变换为
[ 1 0 -2 1 0 0]
[ 0 1 -2 3 1 0]
[ 0 -3 8 -2 0 1]
初等行变换为
[ 1 0 -2 1 0 0]
[ 0 1 -2 3 1 0]
[ 0 0 2 7 3 1]
初等行变换为
[ 1 0 0 8 3 1]
[ 0 1 0 10 4 1]
[ 0 0 2 7 3 1]
初等行变换为
[ 1 0 0 8 3 1]
[ 0 1 0 10 4 1]
[ 0 0 1 7/2 3/2 1/2]
A^(-1) =
[ 8 3 1]
[ 10 4 1]
[7/2 3/2 1/2]
7. 增广矩阵 (A, b) =
[ 1 3 -1 1 2]
[ 2 -1 1 -1 3]
[-1 -2 0 4 1]
初等行变换为
[ 1 3 -1 1 2]
[ 0 -7 3 -3 -1]
[ 0 1 -1 5 3]
初等行变换为
[ 1 0 2 -14 -7]
[ 0 1 -1 5 3]
[ 0 0 -4 32 20]
初等行变换为
[ 1 0 0 2 3]
[ 0 1 0 -3 -2]
[ 0 0 1 -8 -5]
初等行变换为
方程组化为
x1 = 3-2x4
x2 = -2+3x4
x3 = -5+8x4
取 x4 = 0, 得特解 (3, -2, -5, 0)^T;
导出组即
x1 = -2x4
x2 = 3x4
x3 = 8x4
取 x4 = 1, 得Ax = 0 的基础解系 (-2, 3, 8, 1)^T
方程组的通解是 x = k(-2, 3, 8, 1)^T + (3, -2, -5, 0)^T。
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