MATH 405 Study Guide - Midterm Guide: Linear Map

• School: University of Maryland
• Department: Mathematics
• Course: MATH 405
• Professor: All

Document Summary

Assume that v = u w . (a) prove that there are ordered bases , , for v, u, w respectively such that. [tw ] # . (b) let v v and assume that v = u + w where v, u, w are non-zero vectors in v, u, w respectively. Show that v is an eigenvector for t with eigenvalue if and only if u is an eigenvector for tu with eigenvalue and w is an eigenvector for. Tw with eigenvalue : (20 points) consider the linear operator t on p2(r) de ned by. T (f ) = f (1) + f (1)x + f (0)x2, for all f p2(r). De ne the linear operator t on v by t (x) = hx, yiz, for all x v . (you do not need to show that t is linear. )