MATH 304 Quiz: MATH 304 Binghamton Math304 Fall2018 Quiz8

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

Document Summary

L(w2) = 2w2 for some 1, 2 r with t = {w1, w2} independent. (2) (3 pts) find the transition matrices spt and t ps and verify that. Instructions: show all calculations and reasons needed to justify your answers. Let s = {e1, e2} be the standard basis of r2 and let l : r2 r2 be given by. 1 (1) (4 pts) find an eigen-basis, t = {w1, w2}, such that the matrix t [l]t representing. L from t to t is a diagonal matrix d = (cid:20) 1. L(w2) = 2w2 for some 1, 2 r with t = {w1, w2} independent. Solution: we need to nd nonzero vectors such that l(cid:20) a b(cid:21) = (cid:20) b. A(cid:21) = (cid:20) a b(cid:21), that is, b = a and a = b, so b = ( b) = 2b so 2 1 = 0 since b 6= 0.