By using Gauss method you should leave the first line intact (after choosing the good one) and use it to eliminate the others when you done,you passe to the second line and use it to eliminate the rest and so on.
.. and that's what you didn't
ok,suppose we have $\displaystyle \frac{2}{3}x+\frac{5}{3}y-z=0$.
$\displaystyle \vec{x}=(x,y,z)\in span(\left ( 1,2,4 \right ),\left ( 2,1,3 \right ),\left ( 4,-1,1 \right ))$
if and only if $\displaystyle (-\frac{5}{2}y+\frac{3}{2}z,y,z)$=$\displaystyle \alpha_{1}(1,2,4) + \alpha _{2}(2,1,3) + \alpha _{3}(4,-1,1)$
which leads us to another system of equations.
Acutually Raoh if your still around, would you be so kind as to answer another question..(dont see the point in starting a new thread)
It's about linear transformations
(b) LetL : R3 ->R2 be the linear transformation defined by
L(x, y, z) = (x − y, y − z)
(i) Find the standard (2 × 3) matrix representation of L and compute L(1, 1, 1).
I know how to show something is a linear transformation but unsure how to start this question. Just the starting point is all i'm looking for. Maybe i've wasted too much of your time already...