can you solve the system of equations:

x_{1}+ 2x_{3}- x_{4}- x_{5}= 0

2x_{1}+ x_{2}+ x_{3}+ x_{4}= 0

4x_{1}+ 3x_{2}- x_{3}+ 5x_{4}+ 2x_{5}= 0

that's 3 equations in 5 unknowns. assuming the equations are independent (are your 3 vectors linearly independent?), how many "free variables" will you have? how does this help you choose a basis for W?