Let $\underline v = (v\_1, v\_2, v\_3)∈\mathbb{R}^3$ and $\underline w = (w\_1, w\_2)∈\mathbb{R}^2$ be non-zero row vectors. 

Define $T(\underline x) = (\underline v \cdot\underline x)\underline w$

**(a) Show that $Kernel$$(T)$ $= (span$**{$\underline v$}**$)^\bot$**

**(b) Show that $Range(T)=span$**{$\underline w$}

**(c) Show that the standard matrix of $T$ is $\underline w ^t \underline v$**

This is a bonus question set we got in class late last week. I'm going to run over the solution with my tutor on Tuesday, however I'd love to get my head around it prior to that. 

I know that for the last part I would need to show that $T(\underline x)=$$(\underline w ^t \underline v) \underline x$, as $T(\underline x)=A\underline x$ where A is the standard matrix of the linear transformation T. 

Besides that, I have no idea how to go about solving this and any help would be most appreciated.