1. The problem statement, all variables and given/known data Alright, so the question is: Determine a basis for, and solution space of, the following homogenous system: 1 -2 0 -1 = 0 2 -4 0 -2 = 0 -4 8 0 4 = 0 -2 4 0 2 = 0 2. Relevant equations 3. The attempt at a solution Okay. This question is posing some issues for me. First is the fact that all the equations are the same. From looking at a similar problem from the book |1 -2 3||x|=|0| |2 -4 6||y|=|0| |3 -6 9||z|=|0| it appears to me that the professor might have not written it out properly. But anyway, I just assumed that each row represents a variable, x,y,z, and t. Therefore, the solution space is x-y-t=0? If I multiply by the nonexistent 4x1 matrix of x,y,z, and t, then I end up with, once again, four equivalent equations, and the solution space is -2x-4y+2z+t=0. I really just have no understanding of how to do this when all the equations are the same. Help?