MATH 551 Midterm: MATH 551 KSU Sample1Test2WithSolution s07

• School: Kansas State University
• Department: Mathematics
• Course: MATH 551
• Professor: All

Document Summary

First sample of test 2 (chapters 3, 4, and 5) Let t : r2 r3 be the linear transformation given by. 4x2 (i) find a 3 2 matrix a such that t x = ax for every x = (x1, x2) r2. The rst thing to remember is that every linear transformation t can be repre- sented by a certain matrix a. We construct the matrix a as follows: since t is taking values from r2, we consider the canonical basis for r2 which is. We usually denote these vectors by e1 and e2. That is, e1 = [1, 0] and e2 = [0, 1] . Now, the desired matrix a is the one that has t (e1) and t (e2) as columns. T (e1) = t (1, 0) = . T (e2) = t (0, 1) = . Therefore, the matrix a that represents t is. 0 4 (ii) find a basis for range(t ).