Let \(W\) be the span of the vectors \(\vec {v}_1=\begin{bmatrix}1\\2\\-1\\1\end{bmatrix}\) \(\vec {v}_2=\begin{bmatrix}0\\2\\4\\-4\end{bmatrix}\).

In this exercise we will compute a basis for \(W^\perp \).

(a)
Form a matrix \(A\) by using \(\vec {v}_1\) and \(\vec {v}_2\) as the rows of \(A\). Then \(A\) is a \(2 \times 4\) matrix, and \(W^\perp \) is the
Row Column Null
space of \(A\).
(b)
A basis of \(\mbox {null}(W^\perp ):\quad \left \{\begin{bmatrix}5\\\answer {-2}\\1\\0\end{bmatrix}, \begin{bmatrix}-5\\\answer {2}\\0\\1\end{bmatrix} \right \}\)