Question

线性代数。。。。

Answer 1

设 B 的一列为 (x1, x2, x3, x4)^T, 则
x1 + x2 - x3 + 3x4 = 0,
-x1 + 2x2 + x3 + 2x4 = 0.
系数矩阵是 A =
[ 1 1 -1 3]
[-1 2 1 2]
初等行变换为
[ 1 1 -1 3]
[ 0 3 0 5]
x1 + x2 = x3 - 3x4

3x2 = -5x4
得基础解系 (1 0 1 0)^T, (4 5 0 -3)^T,
取 B =
[1 4]
[0 5]
[1 0]
[0 -3]
即可。