Thread: Matrix of Linear Transformation

Determine the matrix representation [T]CB (C is supposed to be the subscript and B the superscript here, sorry) for the linear transformation T and ordered bases B and C.

T: P3 --> P2 given by T(p(x)) = p’(x),
B = {1, x, x^2, x^3}; C = {1, x, x^2}

I really have no idea how to proceed - the textbook is not being very helpful. I would appreciate an explanation rather than a solution, since I have many more of these problems to do. I hope someone can help!

Remember that to find the matrix of linear transformation


Let be a basis for
then
are the columns for the matrix representation of T when expresses in terms of the basis for

This is what I used in the previous problem I helped you with. I hope this gets you started.

So at this point I have e1 = 1, e2 = x and so on for P3. My problem is I have lost track of the geometric meaning of what I am doing, and so I can't see where I am and where I need to go in order to answer the question. If I have these column vectors how to I put them into terms of P2? I know that the kernel will annihilate at least one dimension since it is going into P2 . . .

Originally Posted by dan213

So at this point I have e1 = 1, e2 = x and so on for P3. My problem is I have lost track of the geometric meaning of what I am doing, and so I can't see where I am and where I need to go in order to answer the question. If I have these column vectors how to I put them into terms of P2? I know that the kernel will annihilate at least one dimension since it is going into P2 . . .

Good. So the basis of and the basis of

Now


This is the first two columns just keep going....

Thanks, I was able to figure it out last night with your help on the previous thread. I really appreciate it.