- #1

narfarnst

- 14

- 0

## Homework Statement

Let g(x)=3+x and T(f(x))=f'(x)g(x)+2f(x), and U(a+bx+cx

^{2})=(a+b,c,a-b). So T:P

_{2}(

**R**)-->P

_{2}(

**R**) and U:P

_{2}(

**R**)-->

**R**.

^{3}And let B and

*y*be the standard ordered bases for P

_{2}and

**R**respectively.

^{3}Compute the matrix representation of U (denoted

None, really.

So I get what to do here, I'm just a little hung up with the polynomials.

First, you use the transformations given and the standard bases, and transform the standard bases. B={1,x,x

So U(1)=(1,0,1), U(x)=(1,0,-1), and U(x

And T(1)=2, T(x)=3+3x, and T(x

Now, I'm confused as to how I right the actual matrix of transformation for these. I know what when you're using just numbers (T:R

^{y}_{B}) and T ([T]^{y}_{B}) and their composition UT.## Homework Equations

None, really.

## The Attempt at a Solution

So I get what to do here, I'm just a little hung up with the polynomials.

First, you use the transformations given and the standard bases, and transform the standard bases. B={1,x,x

^{2}} and y={(1,0,0), (0,1,0), (0,0,1)}.So U(1)=(1,0,1), U(x)=(1,0,-1), and U(x

^{2})=(0,1,0).And T(1)=2, T(x)=3+3x, and T(x

^{2})=6x+4x^{2}.Now, I'm confused as to how I right the actual matrix of transformation for these. I know what when you're using just numbers (T:R

^{3}-->R^{2}for example), you write your transformed B basis in terms of coefficients of your*y*basis. But I'm not sure how to do that here.