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## Homework Statement

Let [itex]A \in M_n(F)[/itex] and [itex]v \in F^n[/itex].

Let [itex]v, Av, A^2v, ... , A^{k-1}v[/itex] be a basis, B, of V.

Let[itex] T:V \rightarrow V[/itex] be induced by multiplication by A:T(w) = Aw for w in V. Find [itex][T]_B[/itex], the matrix of T with respect to B.

Thanks in advance

## Homework Equations

[itex][T(w)]_B = [Aw]_B = C^{-1}Aw[/itex]

## The Attempt at a Solution

Can anybody give me a hint please? I'm trying to do this for an hour but I'm not sure how.

From here: http://www.khanacademy.org/math/lin...transformation-matrix-with-respect-to-a-basis

I learned that [itex][T(w)]_B = [Aw]_B = C^{-1}Aw[/itex], where [itex] C= [v| Av| A^2v| ... | A^{k-1}v] [/itex]. But now I don't know what the inverse of C is?

Thanks in advance