# Homework Help: Gaussian Elimination, is this method OK?

1. Oct 10, 2011

### NewtonianAlch

1. The problem statement, all variables and given/known data

A=
<1, -3, -1, 1>
<2, -5, 0, 1>
<-3, 5, -6, 3>

What I did was Row2 = 2*Row1 - Row2 which renders Row2 as: <0, -1, -2, 1>

However in the solutions, Row2 was given as: <0, 1, 2, -1>, which appears to be R2 = -2R1 + R2

I'm guessing it makes no real difference, we were asked to calculate the basis of the kernel(A), to which I got <-8,-3,2,1>$^{T}$ and the solutions gave <8,3,-2,-1>$^{T}$, probably because of the difference in row-reducing the second row.

Am I incorrect?

2. Oct 11, 2011

### Staff: Mentor

No, your work is fine.
I prefer the method used in in the solutions for this problem, though, with R2 being replaced by -2R1 + R2.

The basis vector you got is a multiple of the one shown in the solutions. Both vectors span exactly the same space (a one-dimension subspace of R4).

3. Oct 11, 2011

### NewtonianAlch

Ah yes, that makes sense, it can be gotten by just multiplying by -1. Thanks for pointing that outt.