Let A be an m x n matrix. Show that: ( a ) Ifxε Ν (Α'Α), then AxE R(Α) Ω Ν (A"). (b) N (AT A) = N(A). (c) A and AT A have the same rank.

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Q: please solve this linear algebra problem.

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Q: 8. Let X be an n x p matrix of full column rank. (a) Use Theorem A.23 to show that (In + XX')- = In…

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Q: • Let f(u) = a'u = Li=1 a;Ui for a, u E R“. Calculate Vuf(u).

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

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A: I have used the fact that non zero nilpotent matrix is not Diagonalisable