Show that if the matrix equation XS = B can be solved for X , then X = BS −1 is a solution for any…

1. Show that if the matrix equationXS can be solved forX, thenBS−1 is a solution for any generalized inverse S−1 of S.

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2. Use the result of (a) to derive the expression for P(X|Y)

3. Verify that the steady-state solution of the Kalman recursions is given by

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