Answer:
The Answer is last option
[tex]\left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right]=\left[\begin{array}{ccc}0.5&-3\\0&1\\\end{array}\right]\left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
Step-by-step explanation:
The Answer is last option
[tex]\left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right]=\left[\begin{array}{ccc}0.5&-3\\0&1\\\end{array}\right]\left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
Write The Given Matrix in
AX= B
Now Pre multiplying by [tex]A^{-1}[/tex] we get
[tex]A^{-1}AX=A^{-1}B\\ \\We\ know\\A^{-1}A = I\ and\ IX = X\\\\\therefore X = A^{-1}B\\\\\therefore \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right]=\left[\begin{array}{ccc}0.5&-3\\0&1\\\end{array}\right]\left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
Here,
[tex]A^{-1}=\left[\begin{array}{ccc}0.5&-3\\0&1\end{array}\right]\\\\X=\left[\begin{array}{ccc}x_{1}\\ x_{2}\end{array}\right] \\\\B=\left[\begin{array}{ccc}2\\-3\end{array}\right][/tex]
