Question

大一的线性代数题，求详细答案，谢谢

Answer 1

以下过程供题主参考:

Answer 2

A =
[ 2 -5 -1 -3]
[-3 4 -2 1]
[ 1 2 -1 3]
[-2 15 -6 13]
将第 3 行移至第 1 行，初等行变换为
[ 1 2 -1 3]
[ 0 -9 1 -9]
[ 0 10 -5 10]
[ 0 19 -8 19]
初等行变换为
[ 1 0 -7/9 1]
[ 0 1 -1/9 1]
[ 0 0 -7/18 0]
[ 0 0 -53/171 0]
初等行变换为
[ 1 0 0 1]
[ 0 1 0 1]
[ 0 0 1 0]
[ 0 0 0 0]
r(A) = 3 < 4, 方程组有非零解。方程组化为
x1 = -x4
x2 = -x4
x3 = 0
取 x4 = -1，得基础解系 (1 1 0 -1)^T,
通解是 x = k(1 1 0 -1)^T