From the the following transformations choose those that arelinear. A T : C 1 [0

Question

From the the following transformations choose those that arelinear. A
T : C1[0, 8] ®R where T(f(x)) = f ¢(4) B
T : P2®P3 where T(p(x)) = 3 p ( x ) -x p(x) C
T : P2®R2 whereT(a0+a1x+a2x2) =[3 a1, -a0] D
T : C1[1, 4] ® C[0,10] where T(f(x)) = f(x) +3 f ¢(x) None of the above Please show reason behind answers. A
T : C1[0, 8] ®R where T(f(x)) = f ¢(4) B
T : P2®P3 where T(p(x)) = 3 p ( x ) -x p(x) C
T : P2®R2 whereT(a0+a1x+a2x2) =[3 a1, -a0] D
T : C1[1, 4] ® C[0,10] where T(f(x)) = f(x) +3 f ¢(x) None of the above Please show reason behind answers. A
T : C1[0, 8] ®R where T(f(x)) = f ¢(4) B
T : P2®P3 where T(p(x)) = 3 p ( x ) -x p(x) C
T : P2®R2 whereT(a0+a1x+a2x2) =[3 a1, -a0] D
T : C1[1, 4] ® C[0,10] where T(f(x)) = f(x) +3 f ¢(x) None of the above

Explanation / Answer

(a) without knowing f , we cannot say whether T is alinear transformation or not. (b) since 3p(x)- xp(x) is of degree 3 polynomial , it can bein P3 and linearity of the coefficients ismaintained. so, T is linear. (c) T is a linear transformation. (d) without knowing f , we cannot say T is linear ornot.

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