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. $$A = \begin{bmatrix}1 & 2 & 3 \\ 4 & 5 & 6\end{bmatrix}\ (2×3)$$
      Read matrix A
   2. $$A^T = \begin{bmatrix}1 & 4 \\ 2 & 5 \\ 3 & 6\end{bmatrix}$$
      Rows become columns
   3. $$\begin{bmatrix}1 & 4 \\ 2 & 5 \\ 3 & 6\end{bmatrix}$$
      Result
3. 3. The answer
   $$\begin{bmatrix}1 & 4 \\ 2 & 5 \\ 3 & 6\end{bmatrix}$$

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

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

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