Chapter 3.2, Problem 44E

Consider linearly independent vectors ${\stackrel{\to }{v}}_1,{\stackrel{\to }{v}}_2,\mathrm{...},{\stackrel{\to }{v}}_m$ in ${ℝ}^n$ , and let A be an invertible $m\times m$ matrix. Are thecolumns of the following matrix linearly independent?
   $\left[\begin{array}{cccc}|& |& & |\\ {\stackrel{\to }{v}}_1& {\stackrel{\to }{v}}_2& \cdots & {\stackrel{\to }{v}}_m\\ |& |& & |\end{array}\right]A$