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## Homework Statement

Let B={b1,b2} be a basis for R2 and let T be the linear transformation R2 to R2 such that T(b1)=2b1+b2 and T(b2)=b2. Find the matrix of T relative to the basis B.

## The Attempt at a Solution

I know that the matrix I'm looking for needs to be 2x2 and that the standard matrix of a linear transformation is related to how the transformation would affect the identity matrix. However I don't understand how to relate it to the basis.

My best guess is:

T(b1)=2b1+b2

T(b2)=0b1+b2

so the matrix is [[2,0][1,1]]

But I'm not sure if this is right (if it is, I'm not sure why) or how to check it. Am I on the right track?