Supppose A is an invertible n x n matrix and is an eigenvector of A with associated eigenvalue 7. Convince yourself that is an eigenvector of the following matrices, and find the associated eigenvalues. a. The matrix A6 has an eigenvalue b. The matrix A1 has an eigenvalue c. The matrix A + 81,, has an eigenvalue d. The matrix -6A has an eigenvalue

For the matrix A, find (if possible) a nonsingular matrix P such that PAP is diagonal. (If not possible, enter IMPOSSIBLE.) 2 -2 5 A = 3 -2 L0 -1 2 P = Verify that PAP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP =

Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 077 707 77 7 λ; = For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x;) =

I need help with #5.

Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 044 404 444 For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x) -

Construct a symmetric matrix A with eigenvalues A1 = -3 and 2 = 7 and 1 and V2 = corresponding orthogonal eigenvectors V1 %3D 1 a11 a12 respectively. If A , then the value of a11 is a21 a22 , the value of A12 is A, the value of a21 is and the value of A22 is

Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 033 0 3 3 3 3 λ; = For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x;) =