Exercise 2

Find $M^{\perp}$.

• (a)  $M=\text{$\{\hskip 1.00006pt\begin{pmatrix}x\\ y\end{pmatrix}\mid x+y=0\hskip 1.00006pt\}$}$     (b)  $M=\text{$\{\hskip 1.00006pt\begin{pmatrix}x\\ y\end{pmatrix}\mid-2x+3y=0\hskip 1.00006pt\}$}$     (c)  $M=\text{$\{\hskip 1.00006pt\begin{pmatrix}x\\ y\end{pmatrix}\mid x-y=0\hskip 1.00006pt\}$}$     (d)  $M=\text{$\{\hskip 1.00006pt\vec{0}\,\hskip 1.00006pt\}$}$     (e)  $M=\text{$\{\hskip 1.00006pt\begin{pmatrix}x\\ y\end{pmatrix}\mid x=0\hskip 1.00006pt\}$}$     (f)  $M=\text{$\{\hskip 1.00006pt\begin{pmatrix}x\\ y\\ z\end{pmatrix}\mid-x+3y+z=0\hskip 1.00006pt\}$}$     (g)  $M=\text{$\{\hskip 1.00006pt\begin{pmatrix}x\\ y\\ z\end{pmatrix}\mid\text{$x=0$ and $y+z=0$}\hskip 1.00006pt\}$}$