matrix - Ans.fyi 參考答案

matrix

2008-03-11 5:38 am

Find the eigenvalues of the following pairs of matrices, and use them to decide which of the pairs are similar.

i)
3 2
1 7
and
9 10
-1 1

ii)
1 0 0
4 -3 -2
-4 1 0
and
1 0 0
-2 2 0
4 10 -1

iii)
-2 1 0
0 -2 1
0 0 -1
and
-2 0 0
0 -2 0
0 -1 -1

回答 (1)

myisland8132

2008-03-11 8:47 pm

✔ 最佳答案

(i)
The chacteristic polynomial of the first matrix is

-λ^2-10+19

The chacteristic polynomial of the second matrix is

-λ^2-10+19

So the matrixs are similar

(ii)
The chacteristic polynomial of the first matrix is

(1-λ)(λ+1)(λ+2)

The chacteristic polynomial of the second matrix is
(1-λ)(λ-2)(λ+1)

So the matrixs are not similar

(iii)
The chacteristic polynomial of the first matrix is

-(λ+2)^2(λ+1)

The chacteristic polynomial of the second matrix is
-(λ+2)^2(λ+1)

So the matrixs are similar

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