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The question asks you to simplify the sum of two matrices:

\[
\begin{bmatrix}
1 & 2 & 1 \\
3 & 4 & 0
\end{bmatrix}
+
\begin{bmatrix}
4 & 2 &  \\
1 & 0 & 0 \\
3 & 0
\end{bmatrix}
\]

To add two matrices, simply add their corresponding elements. 

Let's perform the addition:

1. First row, first element: \( 1 + 4 = 5 \)
2. First row, second element: \( 2 + 2 = 4 \)
3. First row, third element: \( 1 + 0 = 1 \)
4. Second row, first element: \( 3 + 1 = 4 \)
5. Second row, second element: \( 4 + 0 = 4 \)
6. Second row, third element: \( 0 + 0 = 0 \)

So the result of the matrix addition is:

\[
\begin{bmatrix}
5 & 4 & 1 \\
4 & 4 & 0
\end{bmatrix}
\]

Now, let's compare this result with the answer options. The correct answer matches option **B**.

Do you have any questions or would you like further explanation? 

Here are five related questions:
1. How do you perform matrix subtraction?
2. What are the conditions for adding two matrices?
3. How do you multiply two matrices?
4. Can you add a 2x3 matrix with a 3x2 matrix?
5. What is the identity matrix in linear algebra?

**Tip:** For matrix addition, both matrices must have the same dimensions, otherwise the operation is undefined.

Simplify the sum of two matrices: [1 2 1; 3 4 0] + [4 2 0; 1 0 0; 3 0 0].

Learn how to simplify the sum of two matrices: [1 2 1; 3 4 0] and [4 2 0; 1 0 0; 3 0 0]. This problem demonstrates the concept of matrix addition and covers the key formula for adding corresponding elements in linear algebra. Suitable for students in Grades 9-12.

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