Let P denote the vector space of all polynomials and f\'(x) denote the derivativ

Question

Let P denote the vector space of all polynomials and f'(x) denote the derivative of f P. State "True" or "False" for each of the following statements. You do not need to justify your answers. T : R^2 rightarrow R^3 defined by T(x, y) = (pi^2x,0,y/2) is a linear transformation. T : R^2 rightarrow R^3 defined by T{x, y) = (x+y, x - y.xy) is a linear transformation. T : R^2 rightarrow R^3 defined by T(x, y) = (1,0.0) is a linear transformation. T : R^2 rightarrow R^3 defined by T(x, y) = (y, x, y) is a linear transformation. T : R^2 rightarrow R^3 defined by T(x, y) = (x,x^2,x^3) is a linear transformation. T : R^2 rightarrow R^3 defined by T(x, y) = (2x+3y,3x + 4y,4x + 5y) is a linear transformation. T : P rightarrow P defined by T(f(x)) = f(0) + f(0)x + f"{0)x^2 is a linear transformation. T : P rightarrow P defined by T(f(x)) = f(1) + f'(2)x + f"(3)x^2 is a linear transformation. T : P rightarrow P defined by T(f(x)) = f(x - 3) is a linear transformation. T : P rightarrow P defined by T(f(x)) = f(x) - 3 is a linear transformation.

Explanation / Answer

1) True

2) False

3) True

4) True

5) False

6) True

7) True

8) True

9) False

10) False

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