https://file.aiquickdraw.com/mathbot/file/17273697081997cvgssq2.jpg

The problem shown in the image asks for the result of matrix multiplication between two matrices, \( A \) and \( B \), where:

\[
A = \begin{pmatrix} 6 & 7 \\ 2 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} -5 \\ 4 \end{pmatrix}
\]

Matrix multiplication between matrix \( A \) (which is a 2x2 matrix) and matrix \( B \) (which is a 2x1 matrix) is possible, and the resulting matrix will be a 2x1 matrix.

### Step-by-Step Solution

To multiply \( A \) and \( B \), we compute the dot product of each row of matrix \( A \) with matrix \( B \):

\[
A \cdot B = \begin{pmatrix} 6 & 7 \\ 2 & 3 \end{pmatrix} \cdot \begin{pmatrix} -5 \\ 4 \end{pmatrix}
\]

#### First element of the resulting matrix:
\[
(6 \times -5) + (7 \times 4) = -30 + 28 = -2
\]

#### Second element of the resulting matrix:
\[
(2 \times -5) + (3 \times 4) = -10 + 12 = 2
\]

### Result:

The result of multiplying matrices \( A \) and \( B \) is:

\[
\begin{pmatrix} -2 \\ 2 \end{pmatrix}
\]

This corresponds to the first option on the left in the given choices.

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Would you like more details on matrix multiplication or further clarification?

Here are five related questions for practice:
1. What happens when you multiply two 2x2 matrices together?
2. How would the result change if matrix \( B \) had different values?
3. Can you find the inverse of matrix \( A \), if it exists?
4. What is the determinant of matrix \( A \)?
5. How does matrix multiplication differ from element-wise multiplication?

**Tip:** Always check the dimensions of matrices before multiplying to ensure that the operation is valid.

Jika A = (6 7; 2 3) dan B = (-5; 4), maka hasil perkalian matriks A dan B adalah?

Learn how to perform matrix multiplication between matrices A and B. This problem involves key linear algebra concepts, such as the dot product and matrix multiplication formula. Suitable for high school students in Grades 10-12.

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