Question

请问各位高手这道线性代数题目怎么做？

如图~做出来了加分！！😊

Answer 1

Answer 2

|A*| = 8，|A*| = |A|^(4-1) = |A|^3 = 8, 则 |A| = 2.
A^(-1) = A*/ |A|, 得 A = |A|(A*)^(-1).
(A*)^(-1) =
[ 1 0 0 0]
[ 0 1 0 0]
[-1 0 1 0]
[ 0 3/8 0 1/8]
则 A = |A|(A*)^(-1) =
[ 2 0 0 0]
[ 0 2 0 0]
[-2 0 2 0]
[ 0 3/4 0 1/4]
AXA^(-1) = XA^(-1) + 3I

AX = X + 3A
(A-I)X = 3A
X = 3(A-I)^(-1)A
A - I =
[ 1 0 0 0]
[ 0 1 0 0]
[-2 0 1 0]
[ 0 3/4 0 -3/4]
(A - I)^(-1) =
[ 1 0 0 0]
[ 0 1 0 0]
[ 2 0 1 0]
[ 0 1 0 -4/3]
X = 3(A-I)^(-1)A =
[ 6 0 0 0]
[ 0 6 0 0]
[ 6 0 6 0]
[ 0 3 0 -1]