I am somehow confused with the given matrix. Because usually, when the system of equations is given as:
ax + by = c
dx + ey = f
the matrix would be written in this manner:
[tex] \left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right] [/tex]
Let me just assume that the arrangement of the given corresponds to this system of equations:
4x + 8y = 0
2x + 5y = 6
So you write it as
[tex] \left[\begin{array}{ccc}4&8&0\\2&5&6\end{array}\right] [/tex]
In order to solve this, the matrix should look like this where x and y are the answers
[tex] \left[\begin{array}{ccc}1&0&x\\0&1&y\end{array}\right] [/tex]
So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be
[tex] \left[\begin{array}{ccc}4&8&0\\0&-2&-12\end{array}\right] [/tex]
Next, Row 1 = (Row 1/4) + R2:
[tex] \left[\begin{array}{ccc}1&0&-12\\0&-2&-12\end{array}\right] [/tex]
Lastly, Row 2 = Row 2 / -2:
[tex] \left[\begin{array}{ccc}1&0&-12\\0&1&6\end{array}\right] [/tex]
Thus, the answer is x=-12 and y=6.
