3. Eigenvalues and Eigenvectors (a) Find the eigenvalues and eigenvectors of the following matrices. 32 5...

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3. Eigenvalues and Eigenvectors (a) Find the eigenvalues and eigenvectors of the following matrices. 32 5 0 . A = • A= = -1 0 1 -3 41 002 H as eigenvector of the following matrix? If so, find the corresponding eigenvalue. (b) Is A [ 1 (c) Prove that if A is invertible with eigenvalue A and corresponding eigenvector u, then A-¹ is an eigenvalue of A-¹ with corresponding eigenvector v. (d) If v is an eigenvector of A with corresponding eigenvalue A and c is a scalar, show that v is an eigenvector of A- cl with corresponding eigenvalue X - c. 3. Eigenvalues and Eigenvectors (a) Find the eigenvalues and eigenvectors of the following matrices. 32 5 0 . A = • A= = -1 0 1 -3 41 002 H as eigenvector of the following matrix? If so, find the corresponding eigenvalue. (b) Is A [ 1 (c) Prove that if A is invertible with eigenvalue A and corresponding eigenvector u, then A-¹ is an eigenvalue of A-¹ with corresponding eigenvector v. (d) If v is an eigenvector of A with corresponding eigenvalue A and c is a scalar, show that v is an eigenvector of A- cl with corresponding eigenvalue X - c.