Exercise 8

Decide if the vector is in the set.

• $\begin{pmatrix}3\\ -1\end{pmatrix}$, $\{\hskip 1.00006pt\begin{pmatrix}-6\\ 2\end{pmatrix}k\mid k\in\mathbb{R}\hskip 1.00006pt\}$

• $\begin{pmatrix}5\\ 4\end{pmatrix}$, $\{\hskip 1.00006pt\begin{pmatrix}5\\ -4\end{pmatrix}j\mid j\in\mathbb{R}\hskip 1.00006pt\}$

• $\begin{pmatrix}2\\ 1\\ -1\end{pmatrix}$, $\{\hskip 1.00006pt\begin{pmatrix}0\\ 3\\ -7\end{pmatrix}+\begin{pmatrix}1\\ -1\\ 3\end{pmatrix}r\mid r\in\mathbb{R}\hskip 1.00006pt\}$

• $\begin{pmatrix}1\\ 0\\ 1\end{pmatrix}$, $\{\hskip 1.00006pt\begin{pmatrix}2\\ 0\\ 1\end{pmatrix}j+\begin{pmatrix}-3\\ -1\\ 1\end{pmatrix}k\mid j,k\in\mathbb{R}\hskip 1.00006pt\}$