Chapter 3.4, Problem 3E

Consider the vectors
${\text{x}}_1=\left(\begin{array}{l}2\\ 1\end{array}\right),{\text{x}}_{\text{2}}=\left(\begin{array}{l}4\\ 3\end{array}\right),{\text{x}}_{\text{3}}=\left(\begin{array}{l}7\\ -3\end{array}\right)$
(a) Show that ${\text{x}}_1$ and ${\text{x}}_{\text{2}}$ form a basis for ${ℝ}^{\text{2}}$ .
(b) Why must ${\text{x}}_1,{\text{x}}_{\text{2}}{\text{,x}}_{\text{3}}$ be linearly dependent?
(c) What is the dimension of Span $\left({\text{x}}_1,{\text{x}}_{\text{2}}{\text{,x}}_{\text{3}}\right)$ ?