c)
so the matrix of T with respect to basis B is
Let be a linear transformation in by .
1)Give the matrix of with respect to the canonical basis .
2)Tell whether is invertible or no and if it is calculate .
3)Give the matrix of with respect to the basis .
4)Give the matrix of T with respect to the basis , .
5)Give the matrix of with respect to the basis , .
------------------------------------------------
My attempt :
1) .
2)As is invertible, so is . I calculated which gave me .
3) I don't know how to do it! I guess I have to express the vectors of the basis of B as linear combination of the canonical vectors... but I'll have 3 scalars and I don't know what to do with them.
4)I think they ask for .
I wrote and I reduced the left matrix. At last the right matrix is the one they ask for and I got it to be .
5) If my attempt for 4) is good, I know how to do this one.
------------------------------------------------------------------
I really need help for part 3), and I'd like to know if I did well what I did. Thanks in advance.
I just called a friend and he told me it's not right...
He told me that what you did here is to find while the exercise asks for .
He told me that to find the columns of , I have to find , and such that for the first column, then and is the second column of the matrix they ask for, and so on.
I'm completely confused. I understand both what you did, but I don't know who's right. I'm at a loss!
This might help:
http://www.cs.berkeley.edu/~demmel/m...ework/HW04.pdf