To solve the equation [tex]\(\left[\begin{array}{cc}-1 & -2 \\ 4 & 8\end{array}\right]+X=\left[\begin{array}{cc}-5 & -1 \\ 2 & 1\end{array}\right]\)[/tex], we can follow these steps:
1. Subtract the given matrix [tex]\(\left[\begin{array}{cc}-1 & -2 \\ 4 & 8\end{array}\right]\)[/tex] from both sides of the equation to isolate [tex]\(X\)[/tex]:
[tex]\[
X = \left[\begin{array}{cc}-5 & -1 \\ 2 & 1\end{array}\right] - \left[\begin{array}{cc}-1 & -2 \\ 4 & 8\end{array}\right]
\][/tex]
2. Subtract corresponding elements of the matrices:
[tex]\[
X = \left[\begin{array}{cc} (-5 - (-1)) & (-1 - (-2)) \\ (2 - 4) & (1 - 8) \end{array}\right]
\][/tex]
3. Simplify the elements:
[tex]\[
X = \left[\begin{array}{cc} (-5 + 1) & (-1 + 2) \\ (2 - 4) & (1 - 8) \end{array}\right] = \left[\begin{array}{cc} -4 & 1 \\ -2 & -7 \end{array}\right]
\][/tex]
Hence, the value of [tex]\(X\)[/tex] is:
[tex]\[
\left[\begin{array}{cc}-4 & 1 \\ -2 & -7\end{array}\right]
\][/tex]
So, the correct answer is:
[tex]\[
\left[\begin{array}{cc}-4 & 1 \\ -2 & -7\end{array}\right]
\][/tex]
