Exercise 7. Let A = 1 2 3 0 1 2. Find the eigenvalues and eigenspaces of A. 3 7 11 Does R³ have a basis of eigenvectors of A? Sol.

Find the complex conjugate eigenvalues and the corresponding eigenvectors of the matrix. 0 4 - 16 0 The eigenvalue(s) is/are. (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)

3 0 Let A = Compute the eigenvalues for A and determine bases for the corresponding -5 -2 eigenspaces. (Use only answer slots needed; leave others blank.) Eigenvalue 1 Eigenspace basis Eigenvalue 2 Eigenspace basis

Let 2. 1 -1 D= 0 3 -1 0 0 2 a. Find the eigenvector(s) associated with the eigenvalue X = 2 1 b. Is the vector an eigenvector of D? Why or why not? 3 c. Based on your work so far do you know if D is diagonalizable? Why or why not.