Chapter 4.7, Problem 39P

PROBLEMS

Prove that if every vector $v$ in a vector space $V$ can be written uniquely as a linear combination of the vectors in $\left\{v_1,v_2,\dots ,v_n\right\}$, then $\left\{v_1,v_2,\dots ,v_n\right\}$ is a basis for $V$.