The linear tranformation L defined by L(p(æ)) = -2p' – 6p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases E = {x³, x², æ, 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) = -9x³ + 14x and g(x) = x² – 3. [L(p(x))]F = %3D [L(g(x))]F

The linear tranformation L defined by L(p(x)) = 12p' 10p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases E = {x³, x², x, 1} and F = S = (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = −12x³ + 9x and g(x) = x² + 8. [L(p(x))]F = {x² + x + 1₂x + 1,1} [L(g(x))]f = =

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'