MATH 225 Spring 2017: Assignment 4 Due at 8:25 a.m. on Friday, June 2, 2017 It is important that you read the assignment submission instructions and suggestions available on LEARN. 1. Let L : R3 M (2, 2) be the linear mapping with matrix 2 1 0 0 1 2 C [L]B = 1 2 1 0 1 1 1 0 1 with respect to bases B and C, where B = 0 , 2 , 1 is a non-standard basis for R3 and 1 0 1 \u001a\u0014 \u0015 \u0014 \u0015 \u0014 \u0015 \u0014 \u0015\u001b 4 1 1 1 0 1 1 0 0 C= , , , is a non-standard basis for M (2, 2). Determine L 5 . 0 0 0 1 0 1 1 0 1 Page 1 a 3 b = (2a b) + (c + 2b)x. Let 2. Consider the linear mapping L : R P1 defined by L c 0 1 1 B = 1 , 0 , 0 be a non-standard basis for R3 and let C = {7 + 2x, 4 x} be a non 0 1 1 standard basis for P1 . Find ]C [L]B , the matrix of L with respect to bases B and C. Page 2 a+d 2b 3. Let L : P3 R4 be the linear mapping defined by L(a + bx + cx2 + dx3 ) = a + d. Determine if L 2c is one-to-one and/or onto. Page 3 4. Let U be the set of all 3 2 matrices with real entries where the sum of the entries in each row is 0. Prove that U is isomorphic to P2 by constructing an explicit isomorphism L : U P2 . Prove that your map L is an isomorphism. Page 4 5. Let L : P5 M (2, 4) be a linear mapping. Prove that L is not onto. Page 5