Matrix Transpose 6B7253

1. **Stating the problem:** We are given a matrix $$A = \begin{bmatrix} 4 & -2 & 7 \\ 5 & 3 & 1 \end{bmatrix}$$. 2. **Understanding the matrix:** This is a $$2 \times 3$$ matrix with 2 rows and 3 columns. 3. **Possible operations:** We can perform operations such as finding the transpose, matrix multiplication (if compatible), or other matrix properties. 4. **Transpose of matrix $$A$$:** The transpose $$A^T$$ is obtained by swapping rows and columns. $$A^T = \begin{bmatrix} 4 & 5 \\ -2 & 3 \\ 7 & 1 \end{bmatrix}$$ 5. **Explanation:** The first row of $$A$$ becomes the first column of $$A^T$$, the second row becomes the second column. 6. **Summary:** The transpose matrix $$A^T$$ is a $$3 \times 2$$ matrix as shown above.