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Transpose [[-1,3,-6,4],[9,5,25,70],[8,-14,-8,12]]

Problem

[[−1,3,−6,4],[9,5,25,70],[8,−14,−8,12]]T

Solution

  1. Identify the dimensions of the original matrix. The given matrix has 3 rows and 4 columns, making it a 3×4 matrix.

  2. Apply the definition of a transpose. To transpose a matrix, the rows of the original matrix become the columns of the new matrix.

  3. Rewrite the first row [−1,3,−6,4] as the first column of the new matrix.

  4. Rewrite the second row [9,5,25,70] as the second column of the new matrix.

  5. Rewrite the third row [8,−14,−8,12] as the third column of the new matrix.

  6. Verify the dimensions of the resulting matrix. The transposed matrix should be a 4×3 matrix.

Final Answer

[[−1,3,−6,4],[9,5,25,70],[8,−14,−8,12]]T=[[−1,9,8],[3,5,−14],[−6,25,−8],[4,70,12]]

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