Consider the matrix 4 1 -3 2 1 A = 1 0 1 3 -1 3 -2 -1 3 (a) Find an invertible matrix P that diagonalizes A, and find P-'AP. (b) Without doing any further calculation, use the results of (a) to determine whether A is invertible. Explain your answer.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Consider the matrix
4.
1
-3 2
1
A =
3
1
1
-1 3
-2
-1
3
(a) Find an invertible matrix P that diagonalizes A, and find P-'AP.
(b) Without doing any further calculation, use the results of (a) to determine whether A is
invertible. Explain your answer.
(c) Without calculating A°, find the eigenvalues of A³ and a basis for each of the eigenspaces.
Transcribed Image Text:Consider the matrix 4. 1 -3 2 1 A = 3 1 1 -1 3 -2 -1 3 (a) Find an invertible matrix P that diagonalizes A, and find P-'AP. (b) Without doing any further calculation, use the results of (a) to determine whether A is invertible. Explain your answer. (c) Without calculating A°, find the eigenvalues of A³ and a basis for each of the eigenspaces.
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