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Matrix Arithmetic

Part 3: Transpose of a matrix

In this section we experiment with the matrices A and B defined in Part 1.

  1. Explain how AT is related to A.

  2. Compute (AT)T. What do you infer? Explain why your observation must hold for any matrix A.

  3. Compute
    4. What do you conclude from these calculations?

  4. The worksheet defines a matrix M with random entries. Evaluate

    5. These products have some special property -- what is it? (Look at the entries of the product matrices.) Check your observation by re-entering the definition of M several times and re-computing the products.

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