To solve for $X$, we need to isolate $X$ by subtracting the matrix on the left side from the matrix on the right side.

Given: [ \left[\begin{array}{rr}5 & 5 & -7 \ 2 & 3 & -6 \end{array}\right] + X = \left[\begin{array}{rr}1 & 1 & 5 \ 4 & -2 & 9\end{array}\right] ]

We can rearrange it to: [ X = \left[\begin{array}{rr}1 & 1 & 5 \ 4 & -2 & 9\end{array}\right] - \left[\begin{array}{rr}5 & 5 & -7 \ 2 & 3 & -6 \end{array}\right] ]

Now, subtract each corresponding element:

1. Top row: $X_{11} = 1 - 5 = -4, \quad X_{12} = 1 - 5 = -4, \quad X_{13} = 5 - (-7) = 5 + 7 = 12$

2. Bottom row: $X_{21} = 4 - 2 = 2, \quad X_{22} = -2 - 3 = -5, \quad X_{23} = 9 - (-6) = 9 + 6 = 15$

Thus, the matrix $X$ is: $X = \left[\begin{array}{rr} -4 & -4 & 12 \\ 2 & -5 & 15 \end{array}\right]$

Would you like further details or have any questions?

Here are some related questions to deepen understanding:

1. How would you add two matrices of different sizes?
2. What are the properties of matrix addition and subtraction?
3. How does scalar multiplication of a matrix differ from matrix addition?
4. What is the significance of matrix dimensions in operations like addition and subtraction?
5. Can matrix addition be used to solve systems of equations?

Tip: Always check matrix dimensions to confirm that addition or subtraction is possible!