\text { Suppose the reduced echelon form a matrix } \boldsymbol{A}=[\boldsymbol{u} \mathbf{v} \mathbf{w}] \text { is }\left[\begin{array}{lll} 1 & 0 & \mathbf{3} \\ 0 & 1 & \mathbf{5} \\ 0

& 0 & 0 \end{array}\right] \text {, where the } \text { vectors } \mathbf{U} \mathbf{V} \text { and } \mathbf{W} \text { form the columns of } \boldsymbol{A} \text {. Show that } W=3 u+5 v \text {. }