https://file.aiquickdraw.com/mathbot/file/172558523744588dqikuc.jpg

We are given two matrices:

\[
A = \begin{pmatrix} 1 & 2 \\ 4 & 3 \end{pmatrix}
\quad \text{and} \quad
B = \begin{pmatrix} 5 & 6 \\ 8 & 7 \end{pmatrix}
\]

The task is to find the value of \( 3A - 2B \).

Let's compute it step by step.

### Step 1: Calculate \( 3A \)
We multiply each element of matrix \( A \) by 3:

\[
3A = 3 \times \begin{pmatrix} 1 & 2 \\ 4 & 3 \end{pmatrix}
= \begin{pmatrix} 3 & 6 \\ 12 & 9 \end{pmatrix}
\]

### Step 2: Calculate \( 2B \)
We multiply each element of matrix \( B \) by 2:

\[
2B = 2 \times \begin{pmatrix} 5 & 6 \\ 8 & 7 \end{pmatrix}
= \begin{pmatrix} 10 & 12 \\ 16 & 14 \end{pmatrix}
\]

### Step 3: Calculate \( 3A - 2B \)
Now, subtract \( 2B \) from \( 3A \):

\[
3A - 2B = \begin{pmatrix} 3 & 6 \\ 12 & 9 \end{pmatrix}
- \begin{pmatrix} 10 & 12 \\ 16 & 14 \end{pmatrix}
= \begin{pmatrix} 3 - 10 & 6 - 12 \\ 12 - 16 & 9 - 14 \end{pmatrix}
= \begin{pmatrix} -7 & -6 \\ -4 & -5 \end{pmatrix}
\]

Thus, the result of \( 3A - 2B \) is:

\[
\begin{pmatrix} -7 & -6 \\ -4 & -5 \end{pmatrix}
\]

Looking at the options in the image, the correct answer is **d**.

Would you like a detailed explanation of any of the steps?

Here are 5 related questions to expand your understanding:
1. How do you multiply a matrix by a scalar?
2. What is the process for subtracting two matrices?
3. How do you verify the dimensions of matrices before adding or subtracting them?
4. Can matrix multiplication (not scalar multiplication) be commutative?
5. How would the result change if we were calculating \( 2A - 3B \) instead?

**Tip:** When subtracting matrices, ensure both matrices have the same dimensions. Otherwise, the operation cannot be performed!

Diberikan dua buah matriks A = [[1, 2], [4, 3]] dan B = [[5, 6], [8, 7]], maka nilai dari 3A - 2B adalah?

Learn how to calculate 3A - 2B for the matrices A = [[1, 2], [4, 3]] and B = [[5, 6], [8, 7]] with a detailed step-by-step solution. This problem involves matrix operations such as scalar multiplication and matrix subtraction. Suitable for students in Grades 9-12.

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