Let B= {$\displaystyle w_1, w_2, ... w_k$} be an othonormal basis for a subspace W and letvbe any vector in W, wherev= $\displaystyle \lambda_1w_1+\lambda_2w_2+...+\lambda_kw_k$.

Show that $\displaystyle |v|=\sqrt{\lambda_1^2+\lambda_2^2+...+\lambda_k^2}$