Transpose [[1,2],[3,4]]

Problem

[[1,2],[3,4]]T

Solution

1. Identify the matrix to be transposed, which is a 2×2 matrix where the first row is (1,2) and the second row is (3,4)

2. Apply the definition of a transpose, which involves switching the row indices with the column indices.

3. Rewrite the first row of the original matrix as the first column of the new matrix.

[[1],[2]]

4. Rewrite the second row of the original matrix as the second column of the new matrix.

[[3],[4]]

5. Combine these into the resulting transposed matrix.

Final Answer

[[1,2],[3,4]]T=[[1,3],[2,4]]

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