Transpose [[1,2,3],[4,5,6],[7,8,0]]

Problem

[[1,2,3],[4,5,6],[7,8,0]]T

Solution

1. Identify the rows and columns of the given 3×3 matrix.

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

3. Rewrite the first row [1,2,3] as the first column of the new matrix.

4. Rewrite the second row [4,5,6] as the second column of the new matrix.

5. Rewrite the third row [7,8,0] as the third column of the new matrix.

Final Answer

[[1,2,3],[4,5,6],[7,8,0]]T=[[1,4,7],[2,5,8],[3,6,0]]

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