A= ( 4 6 1 )  B= ( 2 4 6 ) 
     ( 5 2 3 )       ( 1 8 2 ) 
     ( 7 5 2 )       ( 3 7 1 ) 
tentukanlah: 
a. A+B
b. A-B
c. B-A
d. A-(A+B) 
e. B+(A-B)

Given two 3x3 matrices \( A \) and \( B \):

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

We will calculate the following operations:

### a. \( A + B \)
Matrix addition is done element-wise:
\[
A + B = \begin{pmatrix} 
4+2 & 6+4 & 1+6 \\
5+1 & 2+8 & 3+2 \\
7+3 & 5+7 & 2+1
\end{pmatrix} = \begin{pmatrix}
6 & 10 & 7 \\
6 & 10 & 5 \\
10 & 12 & 3
\end{pmatrix}
\]

### b. \( A - B \)
Matrix subtraction is also done element-wise:
\[
A - B = \begin{pmatrix} 
4-2 & 6-4 & 1-6 \\
5-1 & 2-8 & 3-2 \\
7-3 & 5-7 & 2-1
\end{pmatrix} = \begin{pmatrix}
2 & 2 & -5 \\
4 & -6 & 1 \\
4 & -2 & 1
\end{pmatrix}
\]

### c. \( B - A \)
This is the reverse of part b, calculated as:
\[
B - A = \begin{pmatrix} 
2-4 & 4-6 & 6-1 \\
1-5 & 8-2 & 2-3 \\
3-7 & 7-5 & 1-2
\end{pmatrix} = \begin{pmatrix}
-2 & -2 & 5 \\
-4 & 6 & -1 \\
-4 & 2 & -1
\end{pmatrix}
\]

### d. \( A - (A + B) \)
This expression simplifies as:
\[
A - (A + B) = A - A - B = -B
\]
So:
\[
-B = \begin{pmatrix} 
-2 & -4 & -6 \\
-1 & -8 & -2 \\
-3 & -7 & -1
\end{pmatrix}
\]

### e. \( B + (A - B) \)
This can be simplified as:
\[
B + (A - B) = B + A - B = A
\]
Thus:
\[
A = \begin{pmatrix}
4 & 6 & 1 \\
5 & 2 & 3 \\
7 & 5 & 2
\end{pmatrix}
\]

### Final Results:
- **a.** \( A + B = \begin{pmatrix} 6 & 10 & 7 \\ 6 & 10 & 5 \\ 10 & 12 & 3 \end{pmatrix} \)
- **b.** \( A - B = \begin{pmatrix} 2 & 2 & -5 \\ 4 & -6 & 1 \\ 4 & -2 & 1 \end{pmatrix} \)
- **c.** \( B - A = \begin{pmatrix} -2 & -2 & 5 \\ -4 & 6 & -1 \\ -4 & 2 & -1 \end{pmatrix} \)
- **d.** \( A - (A + B) = \begin{pmatrix} -2 & -4 & -6 \\ -1 & -8 & -2 \\ -3 & -7 & -1 \end{pmatrix} \)
- **e.** \( B + (A - B) = A = \begin{pmatrix} 4 & 6 & 1 \\ 5 & 2 & 3 \\ 7 & 5 & 2 \end{pmatrix} \)

Would you like any further details on the calculations?

### 5 Questions:
1. How do you perform matrix multiplication?
2. What is the determinant of matrix \( A \)?
3. What is the inverse of matrix \( B \), if it exists?
4. How can you find the transpose of a matrix?
5. How do you perform scalar multiplication on a matrix?

### Tip:
Matrix operations like addition and subtraction are only possible for matrices of the same dimensions. Always check the size of matrices before performing these operations!

A= ( 4 6 1 )  B= ( 2 4 6 ) ( 5 2 3 ) ( 1 8 2 ) ( 7 5 2 ) ( 3 7 1 ) tentukanlah: a. A+B b. A-B c. B-A d. A-(A+B) e. B+(A-B)

Explore how to perform matrix operations such as addition and subtraction for two 3x3 matrices A and B. Includes a detailed step-by-step breakdown of A+B, A-B, B-A, A-(A+B), and B+(A-B). Suitable for students in Grades 10-12.

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