Answer:
Option #4:
[tex]X=\left[\begin{array}{ccc}10\\24\end{array}\right][/tex]
Step-by-step explanation:
Start With
[tex]\left[\begin{array}{ccc}5&-2\\2&-1\end{array}\right] \left[\begin{array}{ccc}2\\-4\end{array}\right][/tex]
1. Pivot Element
[tex]P_{1} =a_{1,1}=5[/tex]
[tex]\left[\begin{array}{ccc}5&-2\\2&-1\end{array}\right] \left[\begin{array}{ccc}2\\-24\end{array}\right][/tex]
2. Pivot Element Again
[tex]P_{2} =a_{2,2}=-1[/tex]
[tex]\left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{ccc}-10\\-24\end{array}\right][/tex]
3. Get x1 and x2 Values
[tex]\left \{ {{(-1)*x_{1}=(-10)} \atop {(-1)*x_{2}=(-24)}} \right.[/tex]
[tex]-x_{2} = (-24)\\x_{2} = 24\\\\-x_{1} = (-10)\\x_{1} = 10\\[/tex]
4. Get Answer
[tex]x_{1}=10\\x_{2}=24\\\\X=\left[\begin{array}{ccc}10\\24\end{array}\right][/tex]
