https://file.aiquickdraw.com/mathbot/file/1729624874996x115snfb.jpg

The equation given is:

\[
\begin{bmatrix} 
5 & 5 & -7 \\
2 & 3 & -6
\end{bmatrix} + X = \begin{bmatrix} 
1 & 1 & 5 \\
4 & -2 & 9
\end{bmatrix}
\]

We need to solve for the matrix \( X \). This can be done by subtracting the first matrix from the second matrix:

\[
X = \begin{bmatrix} 
1 & 1 & 5 \\
4 & -2 & 9
\end{bmatrix} - \begin{bmatrix} 
5 & 5 & -7 \\
2 & 3 & -6
\end{bmatrix}
\]

Now, perform element-wise subtraction:

\[
X = \begin{bmatrix} 
1 - 5 & 1 - 5 & 5 - (-7) \\
4 - 2 & -2 - 3 & 9 - (-6)
\end{bmatrix}
\]

Simplifying each element:

\[
X = \begin{bmatrix} 
-4 & -4 & 12 \\
2 & -5 & 15
\end{bmatrix}
\]

Thus, the solution is:

\[
X = \begin{bmatrix} 
-4 & -4 & 12 \\
2 & -5 & 15
\end{bmatrix}
\]

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you solve for a matrix variable when the equation includes subtraction?
2. What are the properties of matrix addition and subtraction?
3. Can you perform matrix addition or subtraction on matrices of different dimensions?
4. How can matrices be used in solving systems of linear equations?
5. How is matrix subtraction related to vector subtraction?

**Tip:** Always check that the matrices have the same dimensions before performing addition or subtraction.

Solve for X in the matrix equation: [[5, 5, -7], [2, 3, -6]] + X = [[1, 1, 5], [4, -2, 9]]

Learn how to solve the matrix equation [[5, 5, -7], [2, 3, -6]] + X = [[1, 1, 5], [4, -2, 9]] by performing matrix subtraction step-by-step. This problem covers important concepts of matrix addition and subtraction, suitable for students in Grades 10-12.

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