ANSWER
[tex] \left[ {\begin{array}{c} x_1 &\\x_2 \end{array} } \right] = \left[ {\begin{array}{cc} 0.5& - 3\\ 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} 2 &\\ - 3 \end{array} } \right][/tex]
EXPLANATION
The given matrix is
[tex] \left[ {\begin{array}{cc} 2 & 6\\ 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} x_1 &\\x_2 \end{array} } \right] = \left[ {\begin{array}{c} 2 &\\ - 3 \end{array} } \right][/tex]
To solve this matrix, we need to multiply both sides of the matrix equation by the inverse of
[tex]\left[ {\begin{array}{cc} 2 & 6\\ 0 & 1 \\ \end{array} } \right][/tex]
The inverse of this matrix is
[tex] \frac{1}{2 \times 1 - 6 \times 0} \left[ {\begin{array}{cc} 1 & - 6\\ 0 & 2 \\ \end{array} } \right] = \left[ {\begin{array}{cc} 0.5& - 3\\ 0 & 1 \\ \end{array} } \right][/tex]
We multiply both sides by the inverse matrix to obtain;
[tex] \left[ {\begin{array}{c} x_1 &\\x_2 \end{array} } \right] = \left[ {\begin{array}{cc} 0.5& - 3\\ 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} 2 &\\ - 3 \end{array} } \right][/tex]
The correct choice is the last option.
