Transpose [[a,b],[c,d]]

Problem

[[a,b],[c,d]]^T

Solution

1. Identify the matrix to be transposed, which is a 2×2 matrix with rows [a,b] and [c,d]

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, [a,b] as the first column of the new matrix.

4. Rewrite the second row of the original matrix, [c,d] as the second column of the new matrix.

Final Answer

[[a,b],[c,d]]^T=[[a,c],[b,d]]

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