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The problem involves matrix multiplication between two matrices, \( P \) and \( Q \), to find matrix \( R \), where:

- Matrix \( P \) represents the production of laptops (first row) and smartphones (second row) in Division A:
  \[
  P = \begin{bmatrix} 
  500 & 300 \\ 
  200 & 400 
  \end{bmatrix}
  \]
- Matrix \( Q \) represents the same production in Division B:
  \[
  Q = \begin{bmatrix} 
  400 & 200 \\ 
  300 & 500 
  \end{bmatrix}
  \]

The matrix \( R \) is the result of the multiplication \( P \times Q \), which gives the total production of laptops and smartphones from both divisions.

Let me calculate matrix \( R \).The matrix \( R \), which represents the total production of laptops and smartphones from both divisions, is:

\[
R = \begin{bmatrix}
290,000 & 250,000 \\
200,000 & 240,000
\end{bmatrix}
\]

This corresponds to option **c** in the given choices.

Would you like a further explanation on matrix multiplication or how this was calculated?

Here are 5 related questions:
1. What are the conditions required for matrix multiplication to be possible?
2. How do matrix dimensions affect the result of multiplication?
3. Can matrix multiplication be done element-wise? Why or why not?
4. How is matrix multiplication used in real-life applications like production analysis?
5. What would happen if matrices \( P \) and \( Q \) had different dimensions?

**Tip:** When multiplying two matrices, ensure the number of columns in the first matrix equals the number of rows in the second matrix.

Sebuah perusahaan teknologi memiliki dua divisi, divisi A dan divisi B. Matriks P menyatakan jumlah produksi laptop (baris pertama) dan smartphone (baris kedua) di divisi A, sedangkan matriks Q menyatakan produksi yang sama di divisi B. Jika P = [[500, 300], [200, 400]] dan Q = [[400, 200], [300, 500]], dan R merupakan hasil kali antara P dan Q yang merupakan total produksi laptop dan smartphone dari kedua divisi, berapakah matriks R?

Learn how to perform matrix multiplication between two matrices representing the production of laptops and smartphones in two divisions. This problem explores key linear algebra concepts and involves calculating the total production using matrix operations. Suitable for high school students in Grades 10-12.

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