https://file.aiquickdraw.com/mathbot/file/1726759393314icfj267c.jpg

Let's work through the questions from the image.

### Question 1:
The matrix represents the price of basic necessities from 2021 to 2024 in the form of a matrix. Looking at the data from the table, the matrix should be structured as follows:

```
      Beras   Gula   Minyak Goreng
2021  7900    8750   8500
2022  8300    9900   9700
2023  9400    10800  10000
2024  10600   10000  10600
```

Based on the available options, **Option A** is the correct answer since it matches the table.

---

### Question 2:
The equation provided is:

\[
\begin{bmatrix} 5 & a & 3 \\ b & 2 & c \end{bmatrix} = \begin{bmatrix} 5 & 2 & 3 \\ 2a & 2 & ab \end{bmatrix}
\]

To solve this, we can equate the corresponding elements in the two matrices:

- From the first row, we have: 
  - \( 5 = 5 \)
  - \( a = 2 \)
  - \( 3 = 3 \)

- From the second row, we have:
  - \( b = 2a = 2(2) = 4 \)
  - \( 2 = 2 \)
  - \( c = ab = (2)(4) = 8 \)

Thus, **c = 8**, and the correct answer is **C**.

---

### Question 3:
The matrix \( A \) is given as:

\[
A = \begin{bmatrix} 1 & 3 \\ 2 & -1 \\ 0 & 4 \end{bmatrix}
\]

We are asked to find the first row of \( A^T \) (the transpose of \( A \)).

To find the transpose of a matrix, we swap rows with columns. Thus:

\[
A^T = \begin{bmatrix} 1 & 2 & 0 \\ 3 & -1 & 4 \end{bmatrix}
\]

The first row of \( A^T \) is \( [1, 2, 0] \), so the correct answer is **A**.

---

Let me know if you'd like further details on any of the solutions!

### 5 Related Questions:
1. How can we find the determinant of a 3x3 matrix?
2. What are the properties of matrix transposition?
3. How do we multiply two matrices together?
4. What is the inverse of a matrix, and how do we calculate it?
5. How does the rank of a matrix affect its solutions in systems of equations?

### Tip:
When dealing with matrices, always ensure that the dimensions are compatible for operations like multiplication and addition.

Hasil penelitian tentang harga – harga bahan pokok selama tahun 2021, 2022, 2023, 2024 di suatu daerah. Jika data di atas disusun dalam bentuk matriks, serta beberapa pertanyaan tentang kesamaan matriks dan transpos matriks.

Learn how to represent price data of basic commodities from 2021 to 2024 in matrix form. Solve matrix transposition and equality problems with detailed explanations and step-by-step solutions. Suitable for Grades 10-12.

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