- #1
PhizKid
- 477
- 1
Homework Statement
Let ##S = \{1, e^x, e^{-x}, e^{2x}, e^{-2x}\}## and ##B = \{1, sinh(x),cosh(x), sinh(2x), cosh(2x)\}##. S spans the vector space V, and a linear transformation T: V -> V is defined by T(y) = y'' - 3y' - 4y.
(a) Find the representation matrix of T with respect to the bases S and B.
(b) Use the change of basis matrix (transition matrix) P, from S to B, to find the representation matrix of T with respect to the bases B and B.
The Attempt at a Solution
(a) I don't understand what it means to find a single transformation matrix for two different bases.
(b) I already found the change of basis matrix P from S to B by representing the elements in S in terms of the ones in B and set them as columns of the matrix P. But again, I don't understand what it means to use this change of basis to find a transformation matrix for two different bases, but this time the two bases are the same bases?