L(p(x)) = - 6p' – 3p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases E = {x³, x2, x, 1} and F' {x2 + x + 1, x + 1, 1} S = (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = 6x³ – 8x and g(æ) = x? + 10. (L(p(x)))F [L(g(x))|F

Find the coordinate matrix of x in R" relative to the basis B. B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)), x = (-4, 19, -8) [x] = 000 11 It 7

2 [H] a) Treating u, v', and w' as vectors, are the following inner products defined? (i) u. v' 6) (True/False) Let u = (ii) v'. u (iii) u - w' v' = [1 3 2], and w' = [5 -1 -1]. b) Treating u, v', and w' as matrices, are the following matrix products defined? (i) uv' (ii) v'u (iii) uw'