https://file.aiquickdraw.com/mathbot/file/17274219968562mozwmid.jpg

To solve the matrix multiplication problem from the image, the matrices given are:

\[
A = \begin{pmatrix} 3 & -5 \\ 2 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 6 & 1 \\ -4 & 0 \end{pmatrix}
\]

### Matrix multiplication \( A \times B \):

The product of two matrices \( A \) and \( B \) is calculated by multiplying the rows of matrix \( A \) by the columns of matrix \( B \).

1. Multiply the first row of \( A \) with the first column of \( B \):
   \[
   (3 \times 6) + (-5 \times -4) = 18 + 20 = 38
   \]
   
2. Multiply the first row of \( A \) with the second column of \( B \):
   \[
   (3 \times 1) + (-5 \times 0) = 3 + 0 = 3
   \]

3. Multiply the second row of \( A \) with the first column of \( B \):
   \[
   (2 \times 6) + (0 \times -4) = 12 + 0 = 12
   \]

4. Multiply the second row of \( A \) with the second column of \( B \):
   \[
   (2 \times 1) + (0 \times 0) = 2 + 0 = 2
   \]

### The resulting matrix is:
\[
A \times B = \begin{pmatrix} 38 & 3 \\ 12 & 2 \end{pmatrix}
\]

Thus, the product of the matrices is:

\[
\boxed{\begin{pmatrix} 38 & 3 \\ 12 & 2 \end{pmatrix}}
\]

Do you want further details or have any questions? Here are related problems for practice:

1. What is the result of multiplying \( A \) by a different matrix, \( C = \begin{pmatrix} 2 & -1 \\ 3 & 4 \end{pmatrix} \)?
2. What happens if you multiply \( B \times A \)?
3. Can you calculate the determinant of matrix \( A \)?
4. What are the conditions for matrix multiplication to be possible between two matrices?
5. How would you compute the inverse of matrix \( B \) (if it exists)?

**Tip**: When multiplying matrices, make sure the number of columns in the first matrix matches the number of rows in the second matrix!

Diketahui matriks A = [3 -5, 2 0] dan B = [6 1, -4 0]. Tentukan perkalian matriks A . B!

Learn how to solve the matrix multiplication problem for A = [3 -5, 2 0] and B = [6 1, -4 0]. This solution provides a step-by-step explanation of the multiplication process, key formulas, and final result. Suitable for high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation