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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 32E
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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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