Question: 4. ASSIGNMENT 2: EIGENVALUES AND EIGENVECTORS 1. Enter the matrix A. 8 33 38 173 -30 -1 -4 0 -25 AOOO 1 5 0 -16

4. ASSIGNMENT 2: EIGENVALUES AND EIGENVECTORS 1. Enter the matrix A. 8 33 38 173 -30 -1 -4 0 -25 AOOO 1 5 0 -16 -19 -86 15 2. Find the characteristic polynomial and factor it via syms x, f=det (x*eye(5)-A), factor(f). Find the eigenvalues of A. 3. Check your work with eig (A). 4. Find the eigenspaces of A, using the methods of Section 7.1. You may use rref, but you should work out the rest by hand. 5. Check your work with [P, D] = eig (A).\f2. First find the characteristic polynomial and factor syms x f=det(x*eye(5)-A) f = x^5 - 7*x^4 + 19*x^3 - 25*x^2 + 16*x - 4 factor (f) ans = [x - 2, x - 2, x - 1, x - 1, x - 1] So, the eigenvalues of A: 2 = 1 and 2

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