Question

急急急！！！大一线性代数，求助啊，拜托各位大神帮我个忙呗！求过程。。。。求过程哟，谢谢哈！采纳最优

急急急！！！大一线性代数，求助啊，拜托各位大神帮我个忙呗！求过程。。。。求过程哟，谢谢哈！采纳最优12题和14题前俩小问，就是打勾的题

Answer 1

12. A^k = O, E-A^k = E,
(E-A)[E+A+A^2+......+A^(k-1)] = E
E-A 可逆，且 (E-A)^(-1) = E+A+A^2+......+A^(k-1)
14 (1) AX = B, X = A^(-1)B , A^(-1) =
[ 3 -5]
[-1 2]
X = A^(-1)B =
[2 -23]
[0 8]
14 (2) XA = B, X = BA^(-1) , (A, E) =
[2 1 -1 1 0 0]
[2 1 0 0 1 0]
[1 -1 1 0 0 1]
初等行变换为
[2 1 -1 1 0 0]
[0 0 1 -1 1 0]
[1 -1 1 0 0 1]
初等行变换为
[1 -1 1 0 0 1]

[0 3 -3 1 0 -2]
[0 0 1 -1 1 0]
初等行变换为
[1 -1 0 1 -1 1]

[0 3 0 -2 3 -2]
[0 0 1 -1 1 0]
初等行变换为
[1 0 0 1/3 0 1/3]

[0 1 0 -2/3 1 -2/3]
[0 0 1 -1 1 0]
A^(-1) =
[ 1/3 0 1/3]

[-2/3 1 -2/3]
[ -1 1 0]
X = BA^(-1) =
[-2 2 1]
[-8/3 5 -2/3]