Gaussian Elimination, is this method OK?

[NewtonianAlch]

Homework Statement

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?

 

[Mark44]

Homework Statement

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?

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).

 

[NewtonianAlch]

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