From the image, the problem asks to find $x$, $y$, and $z$ from the following matrix equation:

$\begin{bmatrix} x & 3 \\ 7 & 2 \end{bmatrix} + \begin{bmatrix} 2 - y & z \\ 2 - z & -x \end{bmatrix} = \begin{bmatrix} 3 & 7 \\ 2 & 0 \end{bmatrix}$

This represents an equation of two matrices, and to solve for $x$, $y$, and $z$, we add the corresponding elements of the two matrices on the left-hand side and equate them to the matrix on the right-hand side. Let's break down the components.

We have:

$\begin{bmatrix} x + (2 - y) & 3 + z \\ 7 + (2 - z) & 2 + (-x) \end{bmatrix} = \begin{bmatrix} 3 & 7 \\ 2 & 0 \end{bmatrix}$

Now, equate corresponding entries:

1. $x + (2 - y) = 3$ (top-left)
2. $3 + z = 7$ (top-right)
3. $7 + (2 - z) = 2$ (bottom-left)
4. $2 + (-x) = 0$ (bottom-right)

Let's solve these four equations step by step.

1. Solve for $y$ from the first equation:

$x + 2 - y = 3 \implies x - y = 1 \quad \text{(Equation 1)}$

2. Solve for $z$ from the second equation:

$3 + z = 7 \implies z = 4 \quad \text{(Equation 2)}$

3. Solve for $z$ from the third equation:

$7 + 2 - z = 2 \implies 9 - z = 2 \implies z = 7 \quad \text{(Contradiction to Equation 2)}$

4. Solve for $x$ from the fourth equation:

$2 - x = 0 \implies x = 2 \quad \text{(Equation 3)}$

With the value of $x = 2$ in hand, let's substitute it back into the first equation to find $y$: $2 - y = 1 \implies y = 1$

So the solution is: $x = 2, \quad y = 1, \quad z = 4$

Would you like more details on any part of the solution?

Here are 5 related questions to expand your understanding:

1. What is the general rule for adding matrices?
2. How can matrix equations like this be used in solving systems of linear equations?
3. Can you solve a similar problem if one matrix is subtracted from another?
4. What happens when matrices have different dimensions?
5. How do we interpret matrix operations in real-world applications?

Tip: When solving matrix equations, always ensure to match corresponding elements correctly for accurate results.