CHEM 131 Midterm: Exam 4b No Solutions Fall 1996

• School: University of Maryland
• Department: Chemistry and Biochemistry
• Course: CHEM 131
• Professor: All

Document Summary

For each of the following matrices a, compute a23 : (18 points) a := (cid:20)1 1. 5 (cid:21) , (18 points) a := (cid:20)5 17. 2 (4 points) for each matrix a above, determine for which vectors v the limit lim n . Problem 2 (18 points). (3 points) de ne eigenvalue. (3 points) de ne eigenvector. (3 points) de ne othogonal matrix. (9 points) using these de nitions, show that every real eigenvalue of an orthogonal matrix has absolute value 1 (and hence equals 1). Let a be the 10 10 matrix: A := (16 points) find a basis for the a-invariant (equivalently a-stable) subspace containing e1 of smallest dimension. If so, nd such a basis. (5 points) a pair of n n matrices c and b are said to commute, if cb = bc. , xn) is a basis obtained by reordering the ele- ments x1, .