https://file.aiquickdraw.com/mathbot/file/1726882183886lqrcjjkl.jpg

The image shows a matrix \( A \) and asks for its transpose.

The matrix \( A \) is given as:
\[
A = \begin{pmatrix} 8 & -5 & -3 \\ 10 & 8 & 4 \end{pmatrix}
\]

To find the transpose of a matrix, we swap the rows and columns. The transpose of matrix \( A \), denoted as \( A^T \), will be:

\[
A^T = \begin{pmatrix} 8 & 10 \\ -5 & 8 \\ -3 & 4 \end{pmatrix}
\]

So, the transpose of the given matrix is:
\[
A^T = \begin{pmatrix} 8 & 10 \\ -5 & 8 \\ -3 & 4 \end{pmatrix}
\]

Would you like more details on matrix transposition or any other related concepts?

### Follow-up Questions:
1. What is the inverse of a matrix, and how do you find it?
2. How does the transpose operation affect the determinant of a matrix?
3. What is the significance of a symmetric matrix in relation to transposition?
4. Can all matrices be transposed? Why or why not?
5. How does matrix transposition apply in linear transformations?

**Tip:** The transpose of a product of two matrices \( (AB)^T \) is the product of the transposes in reverse order: \( (AB)^T = B^T A^T \).

Determine the transpose of the matrix A = [[8, -5, -3], [10, 8, 4]].

Learn how to find the transpose of matrix A = [[8, -5, -3], [10, 8, 4]]. This step-by-step guide explains matrix transposition by swapping rows and columns. Suitable for high school students in Grades 10-12.

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