Answer:
(x, y, z) = (0, 0, 3)
Step-by-step explanation:
The augmented matrix for the system is ...
[tex]\left[\begin{array}{cccc}4&1&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right][/tex]
Subtract 4 times the 3rd row from the first row.
[tex]\left[\begin{array}{cccc}0&9&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right][/tex]
Subtract 2 times the 3rd row from the second row.
[tex]\left[\begin{array}{cccc}0&9&-2&-6\\0&1&3&9\\1&-2&0&0\end{array}\right][/tex]
Subtract 9 times the 2nd row from the first row.
[tex]\left[\begin{array}{cccc}0&0&-29&-87\\0&1&3&9\\1&-2&0&0\end{array}\right][/tex]
Now, the first row can be divided by -29 to give ...
[tex]\left[\begin{array}{cccc}0&0&1&3\\0&1&3&9\\1&-2&0&0\end{array}\right][/tex]
You can subtract 3 times this first row from the second row to get ...
[tex]\left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&-2&0&0\end{array}\right][/tex]
And add 2 times the second row to the third to get ...
[tex]\left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&0&0&0\end{array}\right][/tex]
This matrix now tells you (x, y, z) = (0, 0, 3).
