Exercise 4

Definition 1.1 uses two vectors $\vec{s}$ and $\vec{v}$. Consider the transformation of $\mathbb{R}^{2}$ resulting from fixing

and projecting $\vec{v}$ into the line that is the span of $\vec{s}$. Apply it to these vectors.

• (a)  $\begin{pmatrix}1\\ 2\end{pmatrix}$     (b)  $\begin{pmatrix}0\\ 4\end{pmatrix}$

Show that in general the projection transformation is this.

Express the action of this transformation with a matrix.