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:
x1 - 2x3 - 3x4 = 0
x2 - 3x3 + x4 = 0
2x1 - x2 - x3 - 7x4 = 0
I got a solution of x = x3*(2, 3, 1, 0). I could show closure, but how do you find a basis with just the one vector?