1 2 1 2 -1 Let C = 1 4 Find all eigenvalues and a maximal set T of linearly independent eigenectors for C. Is C diagonalizable? If not, explain why, and if so, find a matrix P such that P-\CP is diagonal and verify that it is.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please use the following:

- The union of the bases for all eigenspaces is a maximal linearly independent set of eigenvectors.

- The matrix (or linear operator) is diagonalizable if and only if the number of vectors in this set is equal to the size of     the matrix (or the dimension of the vector space).

1 2
1 2
2
Let C
-1
-1 1
4
Find all eigenvalues and a maximal set T of linearly independent eigenectors for C.
Is C diagonalizable? If not, explain why, and if so, find a matrix P such that P-CP
is diagonal and verify that it is.
Transcribed Image Text:1 2 1 2 2 Let C -1 -1 1 4 Find all eigenvalues and a maximal set T of linearly independent eigenectors for C. Is C diagonalizable? If not, explain why, and if so, find a matrix P such that P-CP is diagonal and verify that it is.
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