MATH 304 Midterm: MATH 304 Binghamton Math304 Fall2018 Exam3 Solutions

• School: Binghamton University
• Department: Mathematical Science
• Course: MATH 304
• Professor: All

Document Summary

Math 304 fall 2018 exam 3 solutions: (18 points, 3 pts each part) let a, b, c, d be square matrices of the same size such that det(a) = 2, det(b) = 2, det(c) = Solution: det(e) = 0 since there is a dependence relation among the rows of e. (d) if f is a 3 3 matrix such that f3 = 4f, then nd the possible values of det(f). Solution: we have det(f3) = det(4f) so (det(f))3 = 43(det(f)) since a factor of 4 comes out of each of the three rows of 4f. This says det(f)((det(f))2 43) = 0 so either det(f) = 0 or else (det(f))2 = 43 so | det(f)| = 23 = 8. Finally, the possible values of det(f) are 0, 8, 8. Another solution: if f is not invertible, then det(f) = 0. F2 = 4i3 after multiplying f3 = 4f by f 1. So (det(f))2 = 43 = 64 so det(f) = 8.