To solve the matrix equation $X - A = B$ for $X$, we need to isolate $X$. We can do this by adding matrix $A$ to both sides of the equation:

$X = A + B$

Now, let's calculate $A + B$.

Matrices:

$A = \begin{bmatrix} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{bmatrix}, \quad B = \begin{bmatrix} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{bmatrix}$

Matrix Addition $A + B$:

$X = \begin{bmatrix} -3 + (-5) & -7 + (-1) \\ 2 + 0 & -9 + 0 \\ 5 + 3 & 0 + (-4) \end{bmatrix}$

Let's calculate each element:

1. First row: $(-3) + (-5) = -8$, and $(-7) + (-1) = -8$.
2. Second row: $2 + 0 = 2$, and $(-9) + 0 = -9$.
3. Third row: $5 + 3 = 8$, and $0 + (-4) = -4$.

Therefore, the matrix $X$ is:

$X = \begin{bmatrix} -8 & -8 \\ 2 & -9 \\ 8 & -4 \end{bmatrix}$

Would you like further details on this solution, or do you have additional questions?

Related Questions:

1. How do you add matrices with different dimensions?
2. What is matrix subtraction, and how does it differ from matrix addition?
3. How can we check if a matrix addition is performed correctly?
4. What are the properties of matrix addition?
5. Can matrix addition be commutative and associative?

Tip:

When adding or subtracting matrices, make sure the matrices have the same dimensions; otherwise, the operation is undefined.