https://file.aiquickdraw.com/mathbot/file/1726621236834pnkj8xfc.jpg

The image shows two matrices, labeled as \( A \) and \( B \), with the instruction "Tentukan hasil dari matriks," which translates from Indonesian as "Find the result of the matrices." The goal is likely to perform matrix multiplication between these two matrices.

Matrix \( A \) is:
\[
A = \begin{pmatrix} 
2 & 3 \\ 
2 & 4 
\end{pmatrix}
\]

Matrix \( B \) is:
\[
B = \begin{pmatrix} 
0 & 3 \\ 
2 & 1 
\end{pmatrix}
\]

Now, I will compute the product \( AB \), where each element of the resulting matrix is computed by taking the dot product of the corresponding row of \( A \) with the column of \( B \).

Let me calculate it.The result of multiplying matrices \( A \) and \( B \) is:

\[
AB = \begin{pmatrix} 
6 & 9 \\ 
8 & 10 
\end{pmatrix}
\]

Let me know if you'd like more details or if you have any questions!

Here are five related questions for further exploration:
1. How would you compute the determinant of a 2x2 matrix?
2. Can two matrices always be multiplied? Why or why not?
3. What is the inverse of a matrix, and how can it be calculated?
4. What happens if you multiply the matrices \( B \times A \) instead of \( A \times B \)?
5. How can matrix multiplication be used in real-world applications?

**Tip:** Matrix multiplication is not commutative, meaning \( AB \neq BA \) in most cases. Always check the order when multiplying matrices!

Learn how to compute the matrix product of two 2x2 matrices A and B, where matrix A = [[2, 3], [2, 4]] and matrix B = [[0, 3], [2, 1]]. This example demonstrates matrix multiplication, a key concept in linear algebra, suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation