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The second question from your problem set is as follows:

**Problem:**
Identify \( w, x, y, z \) in the equation:

\[
\begin{pmatrix}
w & z \\
y & x
\end{pmatrix}
+
\begin{pmatrix}
3 & 4 \\
2 & 6
\end{pmatrix}
=
\begin{pmatrix}
w+z & z+4 \\
y+2 & x+6
\end{pmatrix}
=
\begin{pmatrix}
3 & 4 \\
2 & 6
\end{pmatrix}
\]

**Solution:**

From the given equation, compare the elements of the matrices on both sides.

1. For the first row, first column: 
   \[
   w + z = 3
   \]
2. For the first row, second column: 
   \[
   z + 4 = 4
   \]
   Solving for \( z \):
   \[
   z = 0
   \]
   Substitute \( z = 0 \) into the first equation:
   \[
   w + 0 = 3 \implies w = 3
   \]

3. For the second row, first column:
   \[
   y + 2 = 2
   \]
   Solving for \( y \):
   \[
   y = 0
   \]

4. For the second row, second column:
   \[
   x + 6 = 6
   \]
   Solving for \( x \):
   \[
   x = 0
   \]

Thus, the values are:
- \( w = 3 \)
- \( x = 0 \)
- \( y = 0 \)
- \( z = 0 \)

---

Would you like further details on how to approach such problems?

Here are some related questions:
1. What is a matrix and how do we add two matrices?
2. How do you perform matrix multiplication?
3. What are the types of matrices, such as symmetric and skew-symmetric matrices?
4. What is the role of determinants in solving systems of equations?
5. How can elementary row transformations help find the inverse of a matrix?

**Tip:** Always check matrix dimensions before performing operations like addition or multiplication to ensure they are valid.

Identify w, x, y, z in the equation involving matrices.

Learn how to solve a matrix equation involving unknowns w, x, y, and z. This example walks through solving a system of linear equations resulting from matrix addition. Suitable for first-year undergraduate students studying basic mathematics or linear algebra.

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