Question

线性代数急救，各位大神帮帮忙

Answer 1

如图。

追答

Answer 2

4. (A, b) =
[1 1 0 2]
[1 -2 3 4]
[2 1 a b]
初等行变换为
[1 1 0 2]
[0 -3 3 2]
[0 -1 a b-4]
初等行变换为
[1 1 0 2]
[0 -1 a b-4]
[0 0 3-3a 14-3b]
方程组有非零解，则 a = 1, b = 14/3.
(A, b) 初等行变换为
[1 0 1 8/3]
[0 1 -1 -2/3]
[0 0 0 0]
方程组化为
x1 = 8/3 - x3
x2 = -2/3 + x3
得特解 (8/3, -2/3, 0)^T
导出租
x1 = -x3
x2 = x3
得基础解系 (-1, 1, 1)^T,
此时通解 x = (8/3, -2/3, 0)^T + k(-1, 1, 1)^T