https://file.aiquickdraw.com/mathbot/file/1726631506186l9x7syt8.jpg

Let's break down the problem based on the image.

We are given matrix \( A \) as:

\[
A = \begin{pmatrix}
-3 & 1 & 0 & 13 & 15 \\
17 & -2 & 16 & 4 & 6 \\
5 & -1 & -7 & 12 & 8 \\
9 & 3 & 10 & -11 & 14
\end{pmatrix}
\]

Here are the tasks provided:

### a. Tentukan ordo matriks A (Determine the order of matrix A)
The order of a matrix refers to the number of rows and columns it has. Matrix \( A \) has 4 rows and 5 columns.  
**Answer**: The order of matrix \( A \) is \( 4 \times 5 \).

### b. Tentukan nilai dari \( 5a_{22} + 3a_{41} - 4a_{34} + 2a_{15} \) (Find the value of the given expression)

Let's break down each element:
- \( a_{22} \) is the element in the 2nd row and 2nd column, which is \( -2 \).
- \( a_{41} \) is the element in the 4th row and 1st column, which is \( 9 \).
- \( a_{34} \) is the element in the 3rd row and 4th column, which is \( 12 \).
- \( a_{15} \) is the element in the 1st row and 5th column, which is \( 15 \).

Now, substitute these values into the given expression:

\[
5a_{22} + 3a_{41} - 4a_{34} + 2a_{15} = 5(-2) + 3(9) - 4(12) + 2(15)
\]

Let's calculate this.

\[
5(-2) = -10, \quad 3(9) = 27, \quad -4(12) = -48, \quad 2(15) = 30
\]

Now, summing them:

\[
-10 + 27 - 48 + 30 = -1
\]

**Answer**: The value is \( -1 \).

### c. Tentukan transpose matriks A (Find the transpose of matrix A)

The transpose of a matrix is obtained by swapping its rows with its columns. The transpose of matrix \( A \) would be:

\[
A^T = \begin{pmatrix}
-3 & 17 & 5 & 9 \\
1 & -2 & -1 & 3 \\
0 & 16 & -7 & 10 \\
13 & 4 & 12 & -11 \\
15 & 6 & 8 & 14
\end{pmatrix}
\]

### d. Tentukan jumlah elemen baris ke-3 (Find the sum of elements in the 3rd row)

The elements in the 3rd row are \( 5, -1, -7, 12, 8 \). Summing them:

\[
5 + (-1) + (-7) + 12 + 8 = 17
\]

**Answer**: The sum of elements in the 3rd row is \( 17 \).

### e. Tentukan jumlah elemen kolom ke-4 (Find the sum of elements in the 4th column)

The elements in the 4th column are \( 13, 4, 12, -11 \). Summing them:

\[
13 + 4 + 12 + (-11) = 18
\]

**Answer**: The sum of elements in the 4th column is \( 18 \).

---

Do you have any questions or want further details? Here are some related questions to expand your understanding:

1. What is the definition of the determinant of a matrix?
2. How is the inverse of a matrix calculated for a \( 2 \times 2 \) matrix?
3. How do we find the rank of a matrix?
4. What is the difference between symmetric and skew-symmetric matrices?
5. How can matrices be used to solve systems of linear equations?

**Tip**: When working with matrices, always ensure that you understand the layout of rows and columns to avoid mixing up indices.

Determine the order of matrix A, solve the expression 5a22 + 3a41 - 4a34 + 2a15, find the transpose of matrix A, sum of elements in the 3rd row, and sum of elements in the 4th column.

Learn matrix operations such as finding the order of matrix A, evaluating algebraic expressions using matrix elements, and calculating the transpose and sum of specific rows and columns. Suitable for students in Grades 9-12.

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