Question: 3. Eigenvalues and Eigenvectors (a) Find the eigenvalues and eigenvectors of the following matrices. 32 5 0 . A = A= = -1 0

3. Eigenvalues and Eigenvectors (a) Find the eigenvalues and eigenvectors of the following matrices. - ( A=left[begin{arra

(b) Is ( left[begin{array}{c}1 -1end{array}right] ) as eigenvector of the following matrix? If so, find the correspo

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- is an eigenvalue of A- 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.

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