https://file.aiquickdraw.com/mathbot/file/1727372296221ph2oake7.jpg

The image contains a matrix multiplication problem where two matrices \( P \) and \( Q \) are given. We are asked to determine the product \( PQ \).

The matrices are as follows:

\[
P = \begin{bmatrix} 2 & 3 \\ 5 & 2 \end{bmatrix}, \quad Q = \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix}
\]

We can calculate \( PQ \) using matrix multiplication rules. Here's the step-by-step process:

\[
PQ = \begin{bmatrix} 2 & 3 \\ 5 & 2 \end{bmatrix} \times \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix}
\]

### Steps:
1. The element at the first row and first column of \( PQ \) is:
   \[
   (2 \times 1) + (3 \times 4) = 2 + 12 = 14
   \]
   
2. The element at the first row and second column of \( PQ \) is:
   \[
   (2 \times 3) + (3 \times 2) = 6 + 6 = 12
   \]

3. The element at the second row and first column of \( PQ \) is:
   \[
   (5 \times 1) + (2 \times 4) = 5 + 8 = 13
   \]

4. The element at the second row and second column of \( PQ \) is:
   \[
   (5 \times 3) + (2 \times 2) = 15 + 4 = 19
   \]

Thus, the product \( PQ \) is:

\[
PQ = \begin{bmatrix} 14 & 12 \\ 13 & 19 \end{bmatrix}
\]

Let me know if you'd like more details on matrix multiplication or anything else!

Here are 5 related questions to think about:
1. What is the difference between matrix multiplication and element-wise multiplication?
2. Can the order of multiplication between two matrices change the result?
3. What conditions must be met for two matrices to be multiplied?
4. How can you compute the determinant of the resulting matrix \( PQ \)?
5. What are some applications of matrix multiplication in real-world problems?

**Tip:** When multiplying matrices, remember that the number of columns in the first matrix must match the number of rows in the second matrix for the multiplication to be valid!

Perhatikan matriks di atas! Tentukan PQ untuk P = [[2, 3], [5, 2]] dan Q = [[1, 3], [4, 2]]

Solve the matrix multiplication of P=[[2,3],[5,2]] and Q=[[1,3],[4,2]] step-by-step, following the rules of matrix multiplication. This problem involves key concepts in linear algebra and is suitable for high school students (Grades 10-12).

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