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Transpose [[-1,8,-47,28],[1,-1,5,-7],[1,-1,1,-6]]

Problem

[[−1,8,−47,28],[1,−1,5,−7],[1,−1,1,−6]]

Solution

  1. Identify the dimensions of the original matrix. The matrix has 3 rows and 4 columns.

  2. Apply the definition of a transpose, which involves switching the row indices with the column indices. The element at position (i,j) in the original matrix will move to position (j,i) in the transposed matrix.

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

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

  5. Rewrite the third row of the original matrix as the third column of the new matrix.

  6. Verify the dimensions of the resulting matrix. The transposed matrix has 4 rows and 3 columns.

Final Answer

[[−1,8,−47,28],[1,−1,5,−7],[1,−1,1,−6]]T=[[−1,1,1],[8,−1,−1],[−47,5,1],[28,−7,−6]]

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