Let P denote the vector space of all polynomials and f'(x)denote the derivative of all numbers in P. State true or false tothe following:
1. T: R^2 --> R^3 defined by T(x,y)=(?^2x,0, y/2) is a linear transformation
2. T: R^2 --> R^3 defined by T(x,y)=(x+y, x-y, xy) is alinear transformation
3. T: R^2 --> R^3 defined by T(x,y)=(1,0,0) is a lineartransformation
4. T: R^2 --> R^3 defined by T(x,y)= (y, x, y) is a lineartransformation
5. T: R^2 --> R^3 defined by T(x,y)= (x, x^2, x^3) is alinear transformation
6. T: R^2 --> R^3 defined by T(x,y)= (2x+3y, 3x+4y, 4x+5y) isa linear transformation
7. T: P --> P defined by T(f(x))= f(0) +f'(0)x + f''(0)x^2 isa linear transformation
8. T: P --> P defined by T(f(x))= f(1) + f'(2) + f''(3)x^2 isa linear transformation
9. T: P --> P defined by T(f(x))= f(x-3) is alinear transformation
10. T: P --> P defined by T(f(x))= f(x)-3 is a lineartransformation
