Exercise 8

Is the given vector in the set generated by the given set?

• $\begin{pmatrix}2\\ 3\end{pmatrix},$ $\{\hskip 1.00006pt\begin{pmatrix}1\\ 4\end{pmatrix},\begin{pmatrix}1\\ 5\end{pmatrix}\hskip 1.00006pt\}$

• $\begin{pmatrix}-1\\ 0\\ 1\end{pmatrix},$ $\{\hskip 1.00006pt\begin{pmatrix}2\\ 1\\ 0\end{pmatrix},\begin{pmatrix}1\\ 0\\ 1\end{pmatrix}\hskip 1.00006pt\}$

• $\begin{pmatrix}1\\ 3\\ 0\end{pmatrix},$ $\{\hskip 1.00006pt\begin{pmatrix}1\\ 0\\ 4\end{pmatrix},\begin{pmatrix}2\\ 1\\ 5\end{pmatrix},\begin{pmatrix}3\\ 3\\ 0\end{pmatrix},\begin{pmatrix}4\\ 2\\ 1\end{pmatrix}\hskip 1.00006pt\}$

• $\begin{pmatrix}1\\ 0\\ 1\\ 1\end{pmatrix},$ $\{\hskip 1.00006pt\begin{pmatrix}2\\ 1\\ 0\\ 1\end{pmatrix},\begin{pmatrix}3\\ 0\\ 0\\ 2\end{pmatrix}\hskip 1.00006pt\}$