Please help me with the following questions, thanks!

Problem 5. One method for computing the determinant of a matrix is so-called cofactor expansion. For a 3 x 3 matrix A, cofactor expansion across the first row gives that a b C det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where A = d e g hi Consider the 3 x 3 matrix A defined by 1 0 0 A = 0 2.5 .5 0 .5 2.5 1. Find pA()), the characteristic polynomial of A. 2. Find the eigenvalues 1, 12, and 13 of A. 3. Find the eigenspaces Ex1, Ex2, and Ex3