https://file.aiquickdraw.com/mathbot/file/1727266869588hhrl3862.jpg

Let's tackle each question from the image one by one. I'll provide solutions based on the given matrix operations.

### Question 11: Diketahui matriks \( G = \begin{bmatrix} 5 & 2 \\ -4 & -7 \end{bmatrix} \) dan \( H = \begin{bmatrix} 7 & -4 \\ 5 & -1 \end{bmatrix} \), Matriks \( H - G \) adalah ...
**Operation:** Subtract \( G \) from \( H \).
\[
H - G = \begin{bmatrix} 7 & -4 \\ 5 & -1 \end{bmatrix} - \begin{bmatrix} 5 & 2 \\ -4 & -7 \end{bmatrix}
= \begin{bmatrix} 7-5 & -4-2 \\ 5-(-4) & -1-(-7) \end{bmatrix}
= \begin{bmatrix} 2 & -6 \\ 9 & 6 \end{bmatrix}
\]
**Answer: C**

### Question 12: Jika matriks \( R = \begin{bmatrix} 1 & -2 \\ -1 & 3 \end{bmatrix} \) dan \( S = \begin{bmatrix} 1 & -3 \\ -2 & 1 \end{bmatrix} \), pernyataan berikut yang salah adalah...
We need to check each statement to find the wrong one.

- \( R - S = \begin{bmatrix} 1-1 & -2-(-3) \\ -1-(-2) & 3-1 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 1 & 2 \end{bmatrix} \)  
- \( S - R = \begin{bmatrix} 1-1 & -3-(-2) \\ -2-(-1) & 1-3 \end{bmatrix} = \begin{bmatrix} 0 & -1 \\ -1 & -2 \end{bmatrix} \)  
- The commutativity checks: \( R - S \neq S - R \).  
Thus, **Answer: E** is the incorrect statement.

### Question 13: Berikut yang **bukan** merupakan sifat operasi perkalian skalar terhadap matriks adalah...
- **Answer: A**. Perkalian skalar tidak komutatif dengan matriks. It follows distributive, associative, and identity properties, but it is not commutative.

### Question 14: Jika matriks \( C = \begin{bmatrix} -1 & -2 \\ 7 & 8 \end{bmatrix} \) dan \( O \) adalah matriks nol, matriks \( C + O \) adalah...
Adding any matrix to a zero matrix results in the matrix itself:
\[
C + O = C = \begin{bmatrix} -1 & -2 \\ 7 & 8 \end{bmatrix}
\]
**Answer: C**

### Question 15: Jika matriks \( R = \begin{bmatrix} 3 & 1 \end{bmatrix} \) dan \( Q = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \), pernyataan yang benar adalah...
We need to check each operation:
- \( R + Q \) is undefined due to incompatible dimensions.
- \( R \times Q = \begin{bmatrix} 3 & 1 \end{bmatrix} \times \begin{bmatrix} 1 \\ 3 \end{bmatrix} = (3 \times 1) + (1 \times 3) = 6 \).
**Answer: C**

Would you like to go through the remaining questions in detail?

Here are 5 related questions to deepen your understanding:
1. What are the properties of matrix subtraction?
2. How does matrix commutativity differ from scalar multiplication?
3. What is the effect of adding a zero matrix to any matrix?
4. How do you determine the dimension compatibility for matrix addition and multiplication?
5. What are the properties of matrix operations, such as associative and distributive laws?

**Tip:** Always ensure that matrix dimensions are compatible before performing operations like addition and multiplication.

Jawablah pertanyaan berikut dengan benar (Matrix Operations: questions 11-19)

This problem set covers key matrix operations, including addition, subtraction, scalar multiplication, and the properties of zero matrices. Learn to solve questions like matrix subtraction, checking matrix commutativity, and scalar operations. Suitable for high school students.

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