https://file.aiquickdraw.com/mathbot/file/1729043105938t3xiphz1.jpg

The problem asks to determine the values of \( a \) and \( b \) based on a matrix equation. The equation shown is:

\[
\begin{pmatrix}
-0 & 3 \\
2b & 4
\end{pmatrix}
= 
\begin{pmatrix}
1 & 3 \\
4 & a
\end{pmatrix}
\]

To solve this, we need to equate corresponding elements of the two matrices.

From the top left corner:
\[
0 = 1 \quad \text{(This seems like an error in the matrix)}
\]
From the top right corner:
\[
3 = 3 \quad \text{(This is correct)}
\]
From the bottom left corner:
\[
2b = 4 \quad \Rightarrow \quad b = 2
\]
From the bottom right corner:
\[
4 = a \quad \Rightarrow \quad a = 4
\]

Thus, the values are:
- \( a = 4 \)
- \( b = 2 \)

Let me know if you need further clarification, or if you'd like more details about matrix equality and how to solve these problems!

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Here are 5 follow-up questions to deepen your understanding:
1. What are the basic properties of matrix equality?
2. How can matrix equations be applied to solve systems of linear equations?
3. Can you find examples of matrix operations in real-world applications?
4. What happens when matrices of different sizes are compared?
5. How do we handle matrix inversion when solving matrix equations?

**Tip:** When equating matrices, always compare elements in the corresponding positions directly to form equations.

Determine the values of a and b from the following matrix equation: 

\[
\begin{pmatrix}
0 & 3 \\
2b & 4
\end{pmatrix}
= 
\begin{pmatrix}
1 & 3 \\
4 & a
\end{pmatrix}
\]


Learn how to solve for the values of a and b in a matrix equation by applying matrix equality principles. This problem involves comparing the corresponding elements of two matrices and solving for unknowns.

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