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In Exercises 23-26, use the method of Example 4.5 to find all of the eigenvalues of the matrix A. Give bases for each of the corresponding eigenspaces. A=[4121]

Show that A=[0110] has no real eigenvalues.

In Exercises 7-12, show that is an eigenvector of A and find one eigenvector corresponding to this eigenvalue. 7.

In Exercises 31-34, find all of the eigenvalues of the matrix A over the indicated p. A=[3140]over5

CAPSTONE Explain how to determine whether an nn matrix A is diagonalizable using a similar matrices, b eigenvectors, and c distinct eigenvalues.

For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.