Question

2. Choose either of them. In each of the following problems, W (a). Find the matrix M of the linear transformation T: V relative to the bases B and C of V and W, respectively. (b). A vector in V is given, verify that (T(7)]c = M(7)B (1). A linear transformation T: P2 R is defined by T (PU) - ( PC ), i.e., 7(a + bé + caº) = [atőte] B = {2,1,1}, c= {{0}][1]} p(t) = 1 + 2+ + 372 -1 -1 (Answer: (a). M= 0 [-1 1 -1 0 1 1 1 1 1 1

Answer 1

2 (a) Find the matrix M for Lineal Transformations T:VTW where B is basis for and C forw Define as TiP > R² LOD FH - 07 as T (Ct) = [phie-T (a tot +C+)= fereated Now B=of tz, t, 13 set is basis for Pos y -: 7(4) = 7(040t+14) = [0]=-*[!]+[}}") T (4)= 7(0+i+top)= [8] --[6]+[:-) T(1) = T(0+02) = [1] = 0[!]+'[i] +a) ... The matrix M (coefficient Matâx) = from 1), (2),(3) (b) let ä = (t)= 1+27+3+ Then TC) = T(4) = TS7= [1:]= 6] Since TCG JEW(R) and set C=f[*], []} is basis for set wie.R² Then T(87)=x[!]+B[] where A, B & calars [8]=[!]+B[i] solve these ar tre! TCP) = -5[ 6346[!] .:. (16) - [] ' J UJ Rescue B = 6 =) 22-5 ( CS$canned with CamScanner

Since si = P(t) EViel But B= stit, is is basis for vier so si=x, t² + Bt+8 (1) where &, Br, scalars H2E+3+²=x,t²t Bit+r(1) comparing coefficients we get X,=3 ñ Then [57] = { Was ETCPP)] = [-] Ako MERJE = [ 7 ][]=[9] Hence we get [T(31]. = M ( Please CSScanned with CamScanner like my Answel.