Consider a system
with the given row-echelon form for its augmented matrix.
The equations for this system are
\(\eqalign{x - 2y + z &= 4\\y + 6z &= - 1\\z &= 2}\)
The last equation says *z* = 2. Substitute this into the second
equation to get
\(\eqalign{y + 6\left( 2 \right) &= - 1\\y &= - 13}\)
Now substitute *z* = 2 and *y* = –13
into the first equation to get
\(\eqalign{x - 2\left( { - 13} \right) + \left( 2 \right) &= 4\\x &= - 24}\)
Thus the solution is *x* = –24, *y* = –13, and *z* =
2. |