Question: Question 4. Define the matrix P by 1/2 1/2 1/2 1/2 1/2 P = 1/2 -1/2 -1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2

Question 4. Define the matrix P by 1/2 1/2 1/2 1/2 1/2 P = 1/2 -1/2 -1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 (a) Compute the product P'P and explain why the result proves the columns of P are orthonormal. (b) What is the inverse of P? (c) Solve the linear system of equations 1 P T2 1 or explain why there are no solutions

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