Transpose of [[1,2],[3,4],[5,6]]: animated lesson

1. 1. The problem
   Worked example

   Transpose Aᵀ: A = [[1, 2], [3, 4], [5, 6]]
2. 2. Step by step
   1. $$A = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 & 6\end{bmatrix}\ (3×2)$$
      Read matrix A
   2. $$A^T = \begin{bmatrix}1 & 3 & 5 \\ 2 & 4 & 6\end{bmatrix}$$
      Rows become columns
   3. $$\begin{bmatrix}1 & 3 & 5 \\ 2 & 4 & 6\end{bmatrix}$$
      Result
3. 3. The answer
   $$\begin{bmatrix}1 & 3 & 5 \\ 2 & 4 & 6\end{bmatrix}$$

   [[1, 3, 5], [2, 4, 6]]

4. 4. Check
   • ✓All arithmetic is exact (fractions, no rounding).

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