Find all the eigenvectors of a corresponding to the

Question

Consider the matrix in image bellow.

A. Find all the eigenvalues of A
B. Find all the eigenvectors of A corresponding to the eigenvalues found in part (a)
C. Show that the eigenvectors in part (b) form a basis of R³.
D. Write v = <5, 6, 0> as a linear combination of the eigenvectors from part (b)
E. Compute the product Av using standard matric multiplication. [use A from image and v from part (d)]
F. Compute Av using the eigenvalues and eigenvectors of A and part (d)