Linear Algebra Linear transformation question tia?

Question

I understand a lot of this if i can get started. But sometimes im used to matrices and its a function, in this case its very odd to me. the question is as follows ...

Determin if the given function T is a linear transformation. Also find A such that T = F(a).

The function is
T:P2 -> by T(A0 + A1x + A2x^2) = (A0 + A2) + 2A1x + (A1 + A2)x^2

I cant even figure out how to start it. I know we need to prove T(u+v), T(u) + T(v), T(ru). Thanks for your help/time.

Answer 1

Well, if you are comfortable with matrices, make it a matrix equation. Using a, b, and c instead of A0, A1, and A2, we have:

T: -->

Let be the first row of T. Then

. = a + c so
x = 1
y = 0
z = 1

Similarly for the other rows of the matrix. So now that you have the corresponding matrix, are you all set?

If not, then work through the examples you've already outlined with and , etc.:

T() = ?
T() = ?
T() = ?
T() = ?