Q10: T/F? Let A be an n x n matrix. Any scalar a is an eigenvalue of A if and only if it is an eigenvalue of AT. 011: if A is a 3 x 3 matrix that has three nonzero eigenvalues r. s, t counting with multiplicities, is A an invertible matrix? If so. what are the eigenvalues of A'{-1}, counting with multiplicities? C' Hill \":7, C311? J" 'r' 012: Compute the characteristic polynomial of the following general 2 x 2 matrix: where a. b. c. d are arbitrary real numbers. Ui:'_.L'L.f1':_,',CllEL3ilg 013: T/F? Let A be an n x n matrix and B be another n x n matrix given by applying a row operation on A. If x is an eigenvector of A, then x is also an eigenvector of B. biljyeung Clitorig ' Q14: Let A be an m x n matrix, and say v_'l, v_n are the columns of A, which are vectors in R'm. Suppose that m > n, and let B be the n x n matrix given by only picking n rows of A out of m total rows. T/F? If det(B) is nonzero, then v_1, ..., v_n are linearly independent. Gslycoing Chang Q15: Let A. B, and C be n x n matrices. T/ F? If C is invertible and AC = CB, then the eigenvalues of A are precisely the eigenvalues of B (with the same multiplicities). Q16: What happens to the answer to 015 it you don't assume that C is invertible? Q17: T/F? if t-'wo n x n matrices A and B have the same characteristic polynomial, then A and B are similar. a