1812Alex

Thanks, you're right. I've looked at the problem again and it seems the provided "solution set" is actually a solution basis obtained be solving the linear system for x2 and x8 and then looking at pairs of variables in the solution for x4 + x5 + x6 + x7 +x8 = 0 by assuming x6=x7=x8, then x4+x5= 0 and so on for all the pairs of that solution.

I'm stuck on a homework question: Show how the following solution set: [x1,x2,x3,x4,x5,x6,x7,x8]^T =[1,-1,0,0,0,0,0,0]^T, [0,-1,1,0,0,0,0,0]^T,[0,0,0,1,-1,0,0,0]^T,[0,0,0,-1,0,1,0,0]^T,[0,0,0,0,-1,0,1,0]^T,[0,0,0,0,0,-1,0,1] is obtained from the two linear equations x1+x2+x3-x4-x5-x6-x7-x8=0 and x4+x5+x6+x7+x8=0. The two equations can be put into a matrix A= [1,1,1,-1,-1,-1,-1,-1,]; [0,0,0,1,1,1,1,1]. Then row 2 is added to row 1 and the following solution is obtained (where v1, v2, .. v6 are arbitrary values) x1=-v1-v2; x2= v1, x3=v2, x4= -v3 -v4 -v5 -v6; x5=v3; x6=v4; x7=v5; x8=v6. But this corresponds to a solution set different than the one provided in the question: [x1,x2,x3,x4,x5,x6,x7,x8]^T = [-1,1,0,0,0,0,0,0]^T, [-1,0,1,0,0,0,0,0]^T, [0,0,0,-1,1,0,0,0]^T, [0,0,0,-1,0,1,0,0]^T, [0,0,0,-1,0,0,1,0]^T,[0,0,0,-1,0,0,0,1]^T. So the problem is that I don't know how to reproduce the given solution set to the given linear equations. We were also told verbally that Excel can be used to help us with this problem set, but I don't see how that can help if I can't even manually reproduce this solution. I've tested the given solution by plugging it into the equations and it seems to work, but I have no clue how to reproduce it.