MATH-0051 Midterm: MATH51 PastExams Sol3-S11
Document Summary
Midterm exam 3 with solutions: (10 points): check following sets of vectors for independence (no partial credit): Hence, these vectors are not linearly independent. (b) 2 . 1: (15 points): (a) find the eigenvalues of the matrix a = . 1 3 (b) find eigenvectors for each eigenvalue of the matrix a. Solution: (a) eigenvalues are 1, 2, 3 since the matrix is lower triangular. (b) by inspection, the eigenvector corresponding to 3 = 3 is corresponding to 2 = 2 is obtained by solving the system . The eigenvector corresponding to 1 = 1 is obtained by solving. 1 we get v = the system . 1 2 v = 0, and we have v = . 1: (10 points): the matrix a = . 1 1 0 has eigenvectors v = . Solution: for v one has value is 2.
