Question

急急急，求线性代数大神，过程详细，谢谢

Answer 1

设 AX = B
则增广矩阵 (A, B) =
[0 3 2 2 0 4]
[1 0 3 1 -2 4]
[2 1 0 1 1 1]
[3 2 1 2 1 3]
初等行变换为
[1 0 3 1 -2 4]
[0 1 -6 -1 5 -7]
[0 2 -8 -1 -5 -9]
[0 3 2 2 0 4]
初等行变换为
[1 0 3 1 -2 4]
[0 1 -6 -1 5 -7]
[0 0 4 1 -15 5]
[0 0 20 5 -15 25]
初等行变换为
[1 0 3 1 -2 4]
[0 1 -6 -1 5 -7]
[0 0 4 1 -15 5]
[0 0 0 0 60 0]
r(A, B) = r(A) = 3 = n, 矩阵方程有唯一解，
故向量组 B 可由向量组 A 线性表示；
设 BY = A
则增广矩阵 (A, B) =
[2 0 4 0 3 2 ]
[1 -2 4 1 0 3 ]
[1 1 1 2 1 0 ]
[2 1 3 3 2 1 ]
初等行变换为
[1 -2 4 1 0 3 ]
[1 1 1 2 1 0 ]
[2 1 3 3 2 1 ]
[2 0 4 0 3 2 ]
初等行变换为
[1 -2 4 1 0 3 ]
[0 3 -3 1 1 -3 ]
[0 5 -5 1 2 -5 ]
[0 4 -4 -2 3 -4 ]
初等行变换为
[1 -2 4 1 0 3 ]
[0 1 -1 1/3 1/3 -1 ]
[0 0 0 -2/3 1/3 0 ]
[0 0 0 -10/3 8/3 0 ]
初等行变换为
[1 -2 4 1 0 3 ]
[0 1 -1 1/3 1/3 -1 ]
[0 0 0 -2 1 0 ]
[0 0 0 0 3 0 ]
r(B, A) = 4 , r(B) = 2, 矩阵方程 BY = A 无解，
则向量组 A 不能由向量组 B 线性表示。

追问

那些初等变换有哪些