- #1
narfarnst
- 14
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Homework Statement
Let g(x)=3+x and T(f(x))=f'(x)g(x)+2f(x), and U(a+bx+cx2)=(a+b,c,a-b). So T:P2(R)-->P2(R) and U:P2(R)-->R3.
And let B and y be the standard ordered bases for P2 and R3 respectively.
Compute the matrix representation of U (denoted yB) and T ([T]yB) 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,x2} and y={(1,0,0), (0,1,0), (0,0,1)}.
So U(1)=(1,0,1), U(x)=(1,0,-1), and U(x2)=(0,1,0).
And T(1)=2, T(x)=3+3x, and T(x2)=6x+4x2.
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:R3-->R2 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.