matrices

Question

The transpose of matrix A = [[1, 2, 3], [4, 5, 6]] is

RankGuru · Accepted Answer

1. **Definition of Transpose**: If $A$ is an $m 	imes n$ matrix, its transpose $A^T$ is an $n 	imes m$ matrix obtained by interchanging rows and columns.
2. **Identify Matrix**: $A = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{bmatrix}$ (Order: $2 	imes 3$).
3. **Conversion**:
   - Row 1 $(1, 2, 3)$ becomes Column 1.
   - Row 2 $(4, 5, 6)$ becomes Column 2.
4. **Result**: $A^T = \begin{bmatrix} 1 & 4 \ 2 & 5 \ 3 & 6 \end{bmatrix}$ (Order: $3 	imes 2$).

Rank Guru

matrices

Select the correct option:

More matrices Practice Questions

If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]], then AB equals

If A is a 3×3 matrix and |A| = 5, then |3A| equals