Exercise 7

The vector is in the set. What value of the parameters produces that vector?

• $\begin{pmatrix}5\\ -5\end{pmatrix}$, $\{\hskip 1.00006pt\begin{pmatrix}1\\ -1\end{pmatrix}k\mid k\in\mathbb{R}\hskip 1.00006pt\}$

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

• $\begin{pmatrix}0\\ -4\\ 2\end{pmatrix}$, $\{\hskip 1.00006pt\begin{pmatrix}1\\ 1\\ 0\end{pmatrix}m+\begin{pmatrix}2\\ 0\\ 1\end{pmatrix}n\mid m,n\in\mathbb{R}\hskip 1.00006pt\}$