Chapter 1.7, Problem 49E

Let $\left\{v_{\text{1}}\text{,}{v}_{\text{2}}{v}_{\text{3}}\right\}$ be a set of nonzero vectors in $R^m$ such that $v_i^T{v}_j=0$ when $i\ne j$. Show that the set is linearly independent. [Hint: Set $a_1{v}_1+a_2{v}_2+a_3{v}_3=\theta$ and consider ${\theta }^T\theta$.]