Question

The linear tranformation L defined by L(p(x)) = -9p' - 6p" maps Pinto P. (a) Find the matrix representation of L with respect to the ordered bases E = {r", 1, 1,1} and F = {2? + +1, 2+1, 1} 0 0 0 S= 0 0 0 (b) Use Part (a) to find the coordinate vectors of L(p()) and L(g(x)) where p(r) = 2.r 13r and g(x) = r? - 5. [L(p()) = 0 L(g(x)) p = Submit answer

Answer 1

I The linear Cranformation L debened by LC PCO) = -9P-6M! Maps Pinto P3 a Find € the Matrin representation of L with respect to the ordered bases {2², 2², a, I} and F = {n+2+1, 1+1, 2 E Transformation - Ang :- Matrin Representation of a T:Vn (F) Bons (4,79,---- Non] Bm = {4, Yg, → Vm (F ym} are ordered basis TH)= a, y, tag, Yg + tami Yom T(NO )= 9gy tagg ggt thing I'm TH;) = 9,2%, tagi Ggt tami Ym Then matrin of T woret Bm and Bm = [T; Bai Bur] = [9.1.com aig ain 1 ago amo ani amm I myn Now L (23) L (2) Lin Scanbed With CamScanner ~9x322 - 6X6 a -97(x2 +2+)-9 (0+1)+36 = -9xq X -6X2 = 019294041) -8(94) +6 -9 = (2+1) + Con 1) - 9x1 = -940 -6X0 = 0 col-1079771) 70(2171) + 0x) CS

:) Mootzini Reparfondation of L writ' E and 1-97 o S = -9-18 136 6 -9 6 Use pare @ to find the Gardinate of L(PO) and Ligon) where Pim) = 293_13 n and gin) = n25. First Find [percs] and [leomy] il () gn3-1BN 9.413-13.11 to = 9.03 ton_13.1 +0.1 [lm] O 1-13 also g(x) No - 5 = 0.723 +1.929 +0.14 - 5 - :: [gm]ę 11 goreng we know that [LC pomo.] S. [Promo] - 0 [L P(m)] -91 -g -18 0 L36 6 -go 0 [LPm)] -54 -18 - 54 -18 39 +117 189 CS Scanned with CamScanner

,[L0- ) ) ] , ; ; . [ om] ܘܙܢ [£&&]]: : -47 - 9 9 8 .18 0 -5 [LI)] - !? ܘ+ 6 ܘ ܕ ;[((»;L] {* [ -I? ܒ ܠ * CS Scanned with CamScanner