(1 point) Supppose A is an invertible n×n matrix and v⃗ is an eigenvector of A with associated eigenvalue 8. Convince yourself that v⃗ is an eigenvector of the following matrices, and find the associated eigenvalues. The matrix A4 has an eigenvalue . The matrix A−1 has an eigenvalue . The matrix A+4In has an eigenvalue . The matrix 5A has an eigenvalue .

By definition, if is an eigenvector of (with associated eigenvalue 8), then

Rinse and repeat to find

so that has a corresponding eigenvalue of 4096.

For this to hold, we require , or . So has a corresonding eigenvalue of 1/8.

so that has an associated eigenvalue of 12.

so the eigenvalue of is 40.

not solvable

step-by-step explanation:

we need more information, or at least an