Gauss-Jordan elimination

Determine which matrices are in reduced echelon form.

1. $\left[\begin{array}{rrr}1&2&0\\ 0&1&7\end{array}\right]$

2. $\left[\begin{array}{rrrr}1&0&0&0\\ 0&0&1&2\\ 0&0&0&0\end{array}\right]$

3. $\left[\begin{array}{rrrrrr}1&1&0&0&0&5\\ 0&0&1&2&0&4\\ 0&0&0&0&1&3\end{array}\right]$

Use Gauss-Jordan elimination to solve the system of equations $-8x+2y+5z=18,-8x+3y+5z=13$, and $-4x+y+5z=19$.

Use Gauss-Jordan elimination to solve the system of equations $3x-y-2z=3$, $y-4z=0$, and $-2x+y=-2$.

Use Gauss-Jordan elimination to solve the system of equations $-9x+15y=66,-11x+18y=79$, $-x+y=4$, and $z=3$.

Use Gauss-Jordan elimination to solve the system of equations $-19x+8y=-108$, $-71x+30y=-404$, $-2x+y=-12$, $4x+z=14$.

Solve the following two systems of equations simultaneously, by using a single augmented matrix with two constant vectors.