Question

Can you solve this using matrices by row operations 4x+y-2z=-6 2x-3y+3z=9 x-2y=0

Answer 1

Answer:

(x, y, z) = (0, 0, 3)

Step-by-step explanation:

The augmented matrix for the system is ...

$\left[\begin{array}{cccc}4&1&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right]$

Subtract 4 times the 3rd row from the first row.

$\left[\begin{array}{cccc}0&9&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right]$

Subtract 2 times the 3rd row from the second row.

$\left[\begin{array}{cccc}0&9&-2&-6\\0&1&3&9\\1&-2&0&0\end{array}\right]$

Subtract 9 times the 2nd row from the first row.

$\left[\begin{array}{cccc}0&0&-29&-87\\0&1&3&9\\1&-2&0&0\end{array}\right]$

Now, the first row can be divided by -29 to give ...

$\left[\begin{array}{cccc}0&0&1&3\\0&1&3&9\\1&-2&0&0\end{array}\right]$

You can subtract 3 times this first row from the second row to get ...

$\left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&-2&0&0\end{array}\right]$

And add 2 times the second row to the third to get ...

$\left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&0&0&0\end{array}\right]$

This matrix now tells you (x, y, z) = (0, 0, 3).