I need to find the set of solutions to a system of linear equations, show that they are a vector space of R^4, and find a basis for them. The equations are:
x_{1} - 2x_{3} - 3x_{4} = 0
x_{2} - 3x_{3} + x_{4} = 0
2x_{1} - x_{2} - x_{3} - 7x_{4} = 0
I got a solution of x = x_{3}*(2, 3, 1, 0). I could show closure, but how do you find a basis with just the one vector?