Chapter 6.3, Problem 11E

Consider a linear transformation $T\left(\stackrel{\to }{x}\right)=A\stackrel{\to }{x}$ from ${ℝ}^2$ to ${ℝ}^2$ . Suppose for two vectors ${\stackrel{\to }{v}}_1$ and ${\stackrel{\to }{v}}_2$ in ${ℝ}^2$ we have $T\left({\stackrel{\to }{v}}_1\right)=3{\stackrel{\to }{v}}_1$ and $T\left({\stackrel{\to }{v}}_2\right)=4{\stackrel{\to }{v}}_2$ . What can you say about $\det A$ ? Justify your answer carefully.