I'm stuck on a homework question:

Show how the following solution set: [k1,k2,k3,k4,k5,k6,k7,k8]^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 k1+k2+k3-k4-k5-k6-k7-k8=0 and

k4+k5+k6+k7+k8=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 isobtained (where v1, v2, .. v6 are arbitrary values) k1=-v1-v2; k2= v1, k3=v2, k4=-v3 -v4 -v5 -v6; k5=v3; k6=v4; k7=v5; k8=v6. But this corresponds to a solutionset different than the one provided in the question: [k1,k2,k3,k4,k5,k6,k7,k8]^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 tothe given linear equations. We were also told verbally that Excel can be usedto help us with this problem set, but I don't see how that can help if I can'teven manually reproduce this solution. I've tested the given solution byplugging it into the equations and it seems to work, but I have no clue how toreproduce it.