Find the invertible matrix P and diagonal matrix D, so that p-1ap = D: A, the first row is 3,1,0, the second row is 0,3,1, and the third row is 0.03

Find the invertible matrix P and diagonal matrix D, so that p-1ap = D: A, the first row is 3,1,0, the second row is 0,3,1, and the third row is 0.03

Because a = 3 1 0
0 3 1
0 0 3
So a is a Jordan matrix of order 3, and a cannot be diagonalized
So we can't find such invertible matrix P and diagonal matrix D such that P ^ - 1 AP = D

If AB = e, then x satisfies
result

A is an invertible matrix
therefore
|1 2 -1
3 -1 0
2 x 1|≠0
=|1 2 -1
3 -1 0
3 x+2 0|≠0
-| 3 -1
3 x+2|≠0
3x+6+3≠0
x≠-3

The following matrices are transformed into standard matrix (ER 0), the first row 2,3,1, - 3,7, the second row 1,2,0, - 2, - 4, the third row 3, - 2,8,3,0, the fourth row 2, - 3,7,4,3
Use elementary transformation to judge whether the following matrices are invertible, such as invertible finding the first row 3,2,1, the second row 3,1,5, the third row 3,2,3

Using elementary transformation to transform matrix 231-37120-2-43-28302-3743, the first line subtracts the second line × 2, the third line subtracts the second line × 3, the fourth line subtracts the second line × 2 ～ 0-11115120-2-40-888120-77811, the second line plus the first line × 2, the third line subtracts the