To solve the equation \( A X = B \) where:
[tex]\[ A = \begin{pmatrix} 4 & 2 \\ -7 & -3 \end{pmatrix} \][/tex]
and
[tex]\[ B = \begin{pmatrix} -3 & 4 \\ -1 & 5 \end{pmatrix} \][/tex]
we need to find the matrix \( X \).
One way to solve this equation is by finding the inverse of matrix \( A \) and then multiplying it by matrix \( B \), because \( A^{-1} A X = A^{-1} B \), which simplifies to \( X = A^{-1} B \). However, we'll outline the result directly.
The solution to the equation \( A X = B \) gives us:
[tex]\[ X = \begin{pmatrix} 5.5 & -11 \\ -12.5 & 24 \end{pmatrix} \][/tex]
By inspecting the given options, this solution can be recognized as:
[tex]\[ \left\lceil 5 \frac{1}{2} \quad -11 \right] \][/tex]
Thus, the answer is:
[tex]\[ \left\lceil 5 \frac{1}{2} \quad -11 \right] \][/tex]
This matches the provided numerical result above. Note that the format slightly differs from standard matrix notation, but the numerical values match.
So the correct choice is:
[tex]\[ \left\lceil 5 \frac{1}{2} \quad -11 \right] \][/tex]
