Question

计算矩阵题，如图

计算矩阵题，如图如图

Answer 1

(1) 3A - X = B, X = 3A - B =
[1 -2 -3]
[11 -2 5]
(2) AY = C 是非齐次线性方程组
(A, C) =
[1 -1 0 1]
[4 0 2 -2]
初等行变换为
[1 -1 0 1]
[0 4 2 -6]
初等行变换为
[1 0 1/2 -1/2]
[0 1 1/2 -3/2]
则 x1 = -1/2 - (1/2)x3, x2 = -3/2 -(1/2)x3
取 x3 = -1， 得特解 (0, -1, -1)^T
导出组 则 x1 = - (1/2)x3, x2 = -(1/2)x3
取 x3 = -2， 得 AY = 0 的基础解系 (1, 1, -2)^T
则 Y = (0, -1, -1)^T + k (1, 1, -2)^T =
[ k ]
[ k-1 ]
[-2k-1]