Chapter 4.5, Problem 50P

Problems

Generalizing the previous exercise prove that if $\left\{v_1,v_2,\mathrm{...},v_k\right\}$ is linearly independent and ${\text{v}}_{k+1}$ is not in span $\left\{v_1,v_2,\mathrm{...},v_k\right\}$ then $\left\{v_1,v_2,\mathrm{...},v_{k+1}\right\}$ is linearly independent.