M-221 Midterm: MATH 221 Montana State Exam4
Document Summary
Show proper work for full credit in problems 2-4: (2pts each) answer true or false. If a is a 3 3 matrix with spectrum a = {1, 2, 3}, then a is guaranteed to be diagonalizable. (b) If there exist a matrix p that diagonalizes a, then a is orthogonally diagonalizable. (c) If a is any n n matrix, then a and at have the same eigenvalues. (d) If a is a 4 4 matrix with spectrum a = {1, 2, 3, 3}, then it is possible that the dimension of. N (a 2i) is equal to 2. (e) If is an eigenvalue of a, then the homogeneous linear system (a i)~x = ~0 has only the trivial solution. (f) If the characteristic polynomial for the matrix a is given by a( ) = ( 1)( 3)2( + 2)3, then a must be invertible: (28pts) given the matrix.
