Finding a matrix with a given rowspace My linear algebra textbook asks,

Find a matrix $A$ that has $V$ as its row space if $V$ is the subspace spanned by
  $$\begin{align}\begin{bmatrix}1\\1\\0\end{bmatrix},\begin{bmatrix}1\\2\\0\end{bmatrix} \text{, and}\begin{bmatrix}1\\5\\0\end{bmatrix}\end{align}$$

(Strang 4e, problem 2.4.17) 
These vectors span the space of all vectors in $\mathbb{R^3}$ whose third entry is $0$, so I answered with this: 
$$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$
The textbook lists this as the correct answer, however:
$$\begin{bmatrix}1 & 1 & 0\end{bmatrix}$$
This seems wrong to me. How can you make $\begin{bmatrix}1 & 2 & 0\end{bmatrix}$ out of $\begin{bmatrix}1 & 1 & 0\end{bmatrix}$? 

You are right. In fact $(1,1,0)^t$ and $(1,2,0)^t$ form a linearly independent set, and so, you can also put the matrix as
$$A = \begin{pmatrix}
1 & 1 & 0 \\
1 & 2 & 0
\end{pmatrix}$$
