A=(1212233512133181)→B=(103001−1000000001)
Where A reduces to B using Gaussian Elimination. I would like to find the null space of A.
What I see here is that x3=0, which means that the first and second row also equals zero (since x = -3x and x2 = x3. While we have our free variable (the zero row) which I can denote as S. Which means that we have a matrice s(0,0,0,1) left. However the book says that x4 is zero and that x3 is our free variable.
What am I doing wrong here? I guess I could switch row 3 and 4 and it would work but why does it give me a different answer that way? Is there any rule that makes requires me to put rows that EQUAL zero in the last and not the rows with 0 inputs that im missing?
