I'm having trouble understanding Row Echelon Form. I'm trying to solve the system
$-2x - 10y - 29z = 5$
$-4x - 19y -56z = -3$
$x + 5y + 15z = 3$
it has the solution $x = ? , y = ? , z = ?$
I put the system into a augmented matrix; I then performed the row operations:
1) $R_2 = 2R_1 - R_2$
2) $R_3 = R_1 + 2R_3$
3) $R_1 = R_1/-2$
4) $R_2 = R_2/-1$
I obtained: $\begin{bmatrix}1&5&29/2&5\\0&1&-27&-8\\0&0&1&8\end{bmatrix}$
REF says :
1) All nonzero rows are above any rows of all zeros
2) Each leading entry of a row is in a column to the right of leading entry above it
3) ALL entries in a column below a leading entry is zero
I'm satisfying all of these requirements for REF form am I not? Why then is $z = 8$ not true??