Chapter 3.2, Problem 37E

Consider a linear transformation T from ${ℝ}^n$ to ${ℝ}^p$ andsome linearly independent vectors ${\stackrel{\to }{v}}_1,{\stackrel{\to }{v}}_2,\mathrm{...},{\stackrel{\to }{v}}_m$ in ${ℝ}^n$ . Are the vectors $T\left({\stackrel{\to }{v}}_1\right),T\left({\stackrel{\to }{v}}_2\right),\mathrm{...},T\left({\stackrel{\to }{v}}_m\right)$ necessarily linearly independent? How can you tell?