1. Let P denote the vector space of all polynomials and f0(x) denote the derivat

Question

1. Let P denote the vector space of all polynomials and f0(x) denote the derivative of f 2 P. State True or False for each of the following statements. You do not need to justify your answers. (1) T : R2 ! R3 de?ned by T(x; y) = (2x; 0; y=2) is a linear transformation. (2) T : R2 ! R3 de?ned by T(x; y) = (x+y; xy; xy) is a linear transformation. (3) T : R2 ! R3 de?ned by T(x; y) = (1; 0; 0) is a linear transformation. (4) T : R2 ! R3 de?ned by T(x; y) = (y; x; y) is a linear transformation. (5) T : R2 ! R3 de?ned by T(x; y) = (x; x2; x3) is a linear transformation. (6) T : R2 ! R3 de?ned by T(x; y) = (2x+3y; 3x+4y; 4x+5y) is a linear transformation. (7) T : P ! P de?ned by T(f(x)) = f(0) + f ' (0)x + f ' '(0)x2 is a linear transformation. (8) T : P ! P de?ned by T(f(x)) = f(1) + f ' (2)x + f ' '(3)x2 is a linear transformation. (9) T : P ! P de?ned by T(f(x)) = f(x -3) is a linear transformation. (10) T : P ! P de?ned by T(f(x)) = f(x) -3 is a linear transformation.

Explanation / Answer

t t t f t f t t f f t

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