- #1
DWill
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Homework Statement
Hi all, we just started doing linear transformations in class and I still don't fully understand them. Here's one question I've been stuck on:
Let P2(x,y) be the vector space of polynomials in the variables x and y of degree at most 2. Recall the monomial basis for this space is {1, x, y, x2, xy, y2}
Let S: P2(x,y) -> P2(x,y) be the linear transformation which swaps the role of x and y in a polynomial. Write the matrix of S with respect to the monomial basis. Note that S is symmetric.
Homework Equations
The Attempt at a Solution
What are the basic steps I need to take to solve problems of this kind? The thing is I don't know how to start and what to do, so if somebody can teach me I will try to do this on my own. Thanks