Chapter 4.3, Problem 3PP

Let ${\text{v}}_1=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$, ${\text{v}}_2=\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]$, and $\text{H}=\left\{\left[\begin{array}{c}\text{s}\\ \text{s}\\ 0\end{array}\right]:\text{s}\text{ in }ℝ\right\}$. Then every vector in H is a linear combination of v₁ and v₂ because

$\left[\begin{array}{c}\text{s}\\ \text{s}\\ 0\end{array}\right]=\text{s}\left[\begin{array}{c}\text{1}\\ \text{1}\\ 0\end{array}\right]+\text{s}\left[\begin{array}{c}\text{0}\\ \text{1}\\ 0\end{array}\right]$

Is {v₁, v₂} a basis for H?