Question

→XCIO Remaining Time: 1 hour, 58 minutes, 48 seconds. Question Completion Status: QUESTION 10 Let T:P2 P2 be the linear transformation defined by T(p(x)) = xp'(3x). Find the matrix [7]g of Trelative to the basis B = (1.x.x?} of P2 o alooo 110 0 0 6 b. none of these cooo 010 006) d. 00 010 0 61 [200 016 Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Close Wind SAMSUNG

Answer 1

Solution Given that T(Pim)) = mp3m) We have to find the matrix [T] B &T relative to the basis B={1,n, n' 12 } of P₂ Now TIP(n)) = np(3n) T(1= np(3x1) = nxo { P13) = 0 de 13)=0 =0 T(n)= np'(3n) = n13=34 :: 2/3) Ed 3n=3 T(N²) = n. p' (3m²) = n. 60= 6n² dr d(3m3=6 du Now T(I) = 0 = 0.1 + 0.71 +0.n? T(n) = 3 - oll +3in toin? 2 T(m²) = 6n² = 0.1toon+6in n? Thus Matrix [1] of T relative to the Basin fin, n? } of l is given by O [118 = 3 0 o 6 Thus None of these is correct answer correct answer ie option ® is

Solutim the matrix We have to find for what value of n nt3 3 T not Invertiable. 7 i J ' 0 7-1 tet ☺ T Now nt3 거 0 2-1 nt3 = 3 n nal 7 We the find determinant of this matrix for Matrix Not Invertible mean's deterimant = 0 3 3 +3) +0 n 7-1 1-019 이후 께 1)=0 1 (n+3)( ^ nina 1.6M-10) -0134-(4-1)) +013-11) (m+3)(02n+1) - n+1) - 0+0=0 O (+3)(72n+1) = nt 3-o or n²n+1=0 n = - 3 n=-(-1) + Ven) 2_4x1x1 2x/ n=-3 or no II 1-4 07 14 J-3 2 2

Solution Given that '. M5-3 n=1tr3i2 2 { ::-1-42? z 1-3 07 n's ! 131 2 Thus for n=-3 or n= trai 2 matrix is not Invertiable. Thus from given option none of these is correct answer. i-e. e. None of these is correct answer