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PROCUREMENT WORK MATRIX

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For a given square matrix A the predicted values of matrix B are: predicted B=A(A'A)^(-1)A'B why is the matrix C=A(A'A)^(-1)A' an idempotent and symmetric matrix?
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lWhat is the PROCUREMENT cost of the below systems?
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Hi! I need help with these two questions. Thanks! :) 1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other matrix, Matrix B (which is 3 x 4 matrix)?

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