The image you've uploaded contains a set of matrix-related problems. Here’s a breakdown of the first few problems, along with their respective questions:

1. Question 1: Given the matrices $A = \begin{bmatrix} 15 & 3 \\ 9 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & x \\ 3 & 10 \end{bmatrix}$, and the matrix $C = \begin{bmatrix} 1 & -4 \\ 3 & -13 \end{bmatrix}$, find the value of $x$ from the equation $A - B = C^1$.

   • Possible answers: $a. 3, b. 5, c. 7, d. 9, e. 11$.

2. Question 2: Given the matrices $A = \begin{bmatrix} 3 & 0 \\ 2 & 5 \end{bmatrix}$, $B = \begin{bmatrix} x & -1 \\ 2 & 3 \end{bmatrix}$, and $C = \begin{bmatrix} 0 & 1 \\ -15 & 5 \end{bmatrix}$, with $A'$ as the transpose of matrix $A$, if $A' \cdot B = C$, what is the value of $x + y$?

   • Possible answers: $a. -4, b. -1, c. 1, d. 5, e. 7$.

3. Question 3: For a 2x2 matrix $X$ satisfying $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix} = X$, the matrix $X$ is:

   • Possible answers: $a. \begin{bmatrix} -6 & -5 \\ 4 & 2 \end{bmatrix}, b. \begin{bmatrix} 12 & 10 \\ 6 & 5 \end{bmatrix}, c. \begin{bmatrix} -6 & -5 \\ 4 & 5 \end{bmatrix}, d. \begin{bmatrix} 12 & 10 \\ 10 & 8 \end{bmatrix}$.

Do you want to work through one of these problems step by step? Feel free to ask for clarification or additional information.

Related Questions:

1. How do you compute the transpose of a matrix?
2. What is the method to find the inverse of a matrix?
3. How can matrix multiplication be applied to solve system of equations?
4. What are the properties of matrix determinants?
5. How do you solve a matrix equation involving identity matrices?

Tip: When dealing with matrix equations, carefully check matrix dimensions to ensure operations like addition, subtraction, and multiplication are valid.