https://file.aiquickdraw.com/mathbot/file/1726888063576ob0mif0o.jpg

The text in the image asks: *"Tentukan transpos matriks berikut,"* which translates to *"Determine the transpose of the following matrices."*

We are given two matrices:

Matrix \( A \):
\[
A = \begin{pmatrix} 3 & -2 \\ 4 & 1 \end{pmatrix}
\]

Matrix \( B \):
\[
B = \begin{pmatrix} 1 & 3 & 5 & 7 \end{pmatrix}
\]

### Transpose of a Matrix

The transpose of a matrix is obtained by swapping its rows and columns. For example:
- If matrix \( A \) is a 2x2 matrix, the transpose \( A^T \) will have its rows become columns and vice versa.
- For matrix \( B \), a row vector, the transpose will turn it into a column vector.

### Solution:

1. **Transpose of Matrix \( A \):**
\[
A^T = \begin{pmatrix} 3 & 4 \\ -2 & 1 \end{pmatrix}
\]

2. **Transpose of Matrix \( B \):**
\[
B^T = \begin{pmatrix} 1 \\ 3 \\ 5 \\ 7 \end{pmatrix}
\]

Would you like a further explanation or any other questions on this topic? 

Here are 5 questions to expand on the concept:

1. What is the difference between a symmetric and non-symmetric matrix?
2. How do you compute the transpose of a 3x3 matrix?
3. What are some properties of transposed matrices?
4. Can a transpose change the determinant of a matrix?
5. How does transposing affect matrix multiplication?

**Tip:** The transpose of a matrix does not change its determinant; \( \det(A^T) = \det(A) \).

Determine the transpose of the given matrices A and B. Matrix A is a 2x2 matrix and matrix B is a row vector. Learn the key concepts of matrix transposition in this problem, suitable for Grades 10-12.

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