Consider the homogeneous system of linear equations $\homosystem{A}$, and suppose that $\vect{u}=\colvector{u_1\\u_2\\u_3\\\vdots\\u_n}$ is one solution to the system of equations. Prove that $\vect{v}=\colvector{4u_1\\4u_2\\4u_3\\\vdots\\4u_n}$ is also a solution to $\homosystem{A}$.