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## Homework Statement

Find the matrix A' for T: R

^{2}-->R

^{2}, where T(x

_{1}, x

_{2}) = (2x

_{1}- 2x

_{2}, -x

_{1}+ 3x

_{2}), relative to the basis B' {(1, 0), (1, 1)}.

## Homework Equations

B' = {(1, 0), (1, 0)} so B'

^{-1}= {(1, -1), (0, 1)}.

## The Attempt at a Solution

I'm confused at what

*exactly*a transform matrix relative to a given basis is to mean. Does this mean that some vector v

_{B'}, when multiplied by A', will equal T(v)

_{B'}? I have the solution from the book: B

^{-1}AB', but if I had to put in English what it looks to me that this does: B'

^{-1}converts v

_{std}to v

_{B'}, then A is the transform matrix which should take v

_{std}and output T(v)

_{std}, then B' will convert v

_{B'}to v

_{std.}It therefore look as if this will take vectors in standard bases and output them in standard bases after transforming? That can't be right because the answer given is not the same as the transform. What is the question asking, exactly?