Answer
A=$\left[\begin{array}{lll}
1 & -1 & 0\\
2 & 1 & 1\\
0 & 5 & -4\\
0 & 0 & 1
\end{array}\right]$
Work Step by Step
The given set, $W\subset \mathbb{R}^{4}$.
x$\in$W $\Rightarrow$ x$=b\left[\begin{array}{l}
1\\
2\\
0\\
0
\end{array}\right]+c\left[\begin{array}{l}
-1\\
1\\
5\\
0
\end{array}\right]+d\left[\begin{array}{l}
0\\
1\\
-4\\
1
\end{array}\right]$
By definition, on p.203
The column space of an m$\times$n matrix A, written as Col A, is the set of all linear combinations of the columns of A.
$W=$Col A, where
A=$\left[\begin{array}{lll}
1 & -1 & 0\\
2 & 1 & 1\\
0 & 5 & -4\\
0 & 0 & 1
\end{array}\right]$
