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buatlah penyederhanaan dari masing-masing operasi berikut

From the image, the question asks to simplify the given mathematical expressions. The expressions are listed in sections (a), (b), and (c). Here's the transcription of the problems:

1. **Buatlah penyederhanaan dari masing-masing operasi berikut:**
   - (a) \( \left( \begin{array}{cc} 1 & 1 \\ 3 & 2 \end{array} \right) \times \left( \begin{array}{cc} 1 & -1 \\ 1 & 4 \end{array} \right) \)
   - (b) \( \sqrt{5} + 3 \quad \text{and} \quad \sqrt{5} - 3 \)
   - (c) \( 2 + 3 \quad \text{and} \quad 1 + \frac{5}{2} \)

Let's go through them step by step.

### (a) Matrix Multiplication:
We are asked to simplify the multiplication of two 2x2 matrices.

The matrices are:
\[
A = \begin{pmatrix} 1 & 1 \\ 3 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & -1 \\ 1 & 4 \end{pmatrix}
\]

To multiply \(A\) and \(B\), we use the matrix multiplication rule:
\[
C = A \times B = \begin{pmatrix} 
(1 \times 1 + 1 \times 1) & (1 \times -1 + 1 \times 4) \\
(3 \times 1 + 2 \times 1) & (3 \times -1 + 2 \times 4)
\end{pmatrix}
\]
Simplifying:
\[
C = \begin{pmatrix} 
(1 + 1) & (-1 + 4) \\
(3 + 2) & (-3 + 8)
\end{pmatrix}
= \begin{pmatrix} 
2 & 3 \\
5 & 5
\end{pmatrix}
\]

### (b) Simplifying Radicals:
We are asked to simplify two expressions involving square roots.

- \( \sqrt{5} + 3 \) remains as it is, because it is already simplified.
- \( \sqrt{5} - 3 \) also remains as it is, since it cannot be simplified further.

### (c) Arithmetic Operations:
There are two simple arithmetic operations.

1. \( 2 + 3 = 5 \)
2. \( 1 + \frac{5}{2} = 1 + 2.5 = 3.5 \)

### Final Results:
1. **Matrix multiplication result**:
   \[
   \begin{pmatrix} 2 & 3 \\ 5 & 5 \end{pmatrix}
   \]
2. **Square root expressions**:
   - \( \sqrt{5} + 3 \)
   - \( \sqrt{5} - 3 \)
3. **Arithmetic results**:
   - \( 2 + 3 = 5 \)
   - \( 1 + \frac{5}{2} = 3.5 \)

Would you like further explanations or details on any of these steps?

Here are some related questions you might consider:
1. What are the properties of matrix multiplication?
2. How can radicals be simplified further in general?
3. What are some examples where radicals are combined in expressions?
4. How do matrix operations apply to transformations in geometry?
5. What is the significance of arithmetic fractions in algebra?

**Tip:** In matrix multiplication, the order of multiplication matters because it is not commutative. This means \( A \times B \neq B \times A \) in general.

Learn how to simplify matrix multiplication, square root expressions, and basic arithmetic operations. This step-by-step guide covers key mathematical concepts such as multiplying 2x2 matrices, simplifying sqrt(5) + 3, and solving simple arithmetic. Suitable for Grades 9-10.

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