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## Homework Statement

[PLAIN]http://img219.imageshack.us/img219/2950/linl.jpg [Broken]

## Homework Equations

## The Attempt at a Solution

Is this how I do

**part (iii)**?

From (ii) I get:

[itex]M^{\mathcal C}_{\mathcal C} (\phi) = \begin{bmatrix} 1 & 3 & 2 \\ 1 & -3 & 0 \\ 0 & 0 & 2 \end{bmatrix}[/itex]

**3**(iii)

[itex]M^{\mathcal C}_{\mathcal C} (\phi) {\bf v} = {\bf w}[/itex] where [itex]{\bf w}[/itex] is the coordinate vector of [itex]\phi (v)[/itex] with respect to [itex]\mathcal C[/itex] and [itex]{\bf v}[/itex] is the coordinate vector of [itex]v\in V[/itex] .

[itex]{\bf v} = \begin{bmatrix} 1 \\ -3 \\ \pi \end{bmatrix}[/itex]

So [itex]{\bf w} = \begin{bmatrix} 1 & 3 & 2 \\ 1 & -3 & 0 \\ 0 & 0 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ -3 \\ \pi \end{bmatrix} = \begin{bmatrix} 2\pi -8 \\ 10 \\ 2\pi \end{bmatrix}[/itex]

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