Transpose of a Matrix Calculator
Set up a matrix A (m×n), fill it, and compute its transpose AT.
Step-by-step method
- Write the matrix A.
- Swap rows and columns to form Aᵀ.
- Read off the transposed matrix.
Transpose formula
a | b | c |
d | e | f |
a | d |
b | e |
c | f |
Example 1: A (2×3) → Aᵀ (3×2)
Step 1 - Write the matrix A.
In this problem: A has size 2×3.
1 | 2 | 3 |
4 | 5 | 6 |
Step 2 - Swap rows and columns to form Aᵀ.
In this problem: AT will have size 3×2.
Step 3 - Read off the transposed matrix.
In this problem: Write the new matrix by swapping indices.
1 | 4 |
2 | 5 |
3 | 6 |
Final answer:
1 | 4 |
2 | 5 |
3 | 6 |
Example 2: A (3×2) → Aᵀ (2×3)
Step 1 - Write the matrix A.
In this problem: A has size 3×2.
-2 | 0 |
7 | 3 |
1 | -4 |
Step 2 - Swap rows and columns to form Aᵀ.
In this problem: AT will have size 2×3.
Step 3 - Read off the transposed matrix.
In this problem: Write the new matrix by swapping indices.
-2 | 7 | 1 |
0 | 3 | -4 |
Final answer:
-2 | 7 | 1 |
0 | 3 | -4 |
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