Question

-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2

Answer 1

Let l: IR^3 rightarrow IR^2 be a L.T given L (3 2 7) = (5 2), L(2 1 0) = (1 3), L(5 4 8) = (4 6) (a) Find the matrix A that represents L with respect to the basis v = [(3 2 7),(2 1 6),(5 4 8) and standard basis of IR^2 (a)matrix L w r t Basis U and F is A = matrix (5 2 1 3 4 6) (1,0,0) = a (3,2,7) + b (2,1,6) + c(5,4,8) (1,0,0) = (3a + 2b + c, 2a + b + 4c, 7a + 6b + 8c) 3a + 2b + c = 1 thatis 1 2a + b + 4c = 0 thatis 2 7a + 6b + 8c = 0 thatis 3 a = 16/19, b = -12/19, c = -5/19 therefore L (1,0,0) = 16/19 L (2,1,6) - 5/19 L (5,4,8) = 16/19 (5,2) - 12/19 (1,3) -