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  3. question 4 a consider the following matrices b21 3...

Question: question 4 a consider the following matrices b21 3...

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QUESTION 4 (a) Consider the following matrices , B21 3, and C- Compute (A B) and (B & A) 2B-B-B (b) Let C be defined by C-B 2B -Bwhere B- -B -B 2B Find the characteristic roots of C (c) Define Ai -J and A, Show that (0) Ai is a symmetric and idempotent matrıx (n) Azis a symmetric and idempotent matrıx

QUESTION 3 (a) Let A be an m x n matrx and A be any c-inverse of A Suppose a solution exists to the system Ax- g Prove that for each and every n x 1 vector h, the vector x is a solution where (b) ) Prove that a necessary and sufficient condition for a solution to exıst to the system Ax -g is that there is a c-inverse, Ac of A such that AA g-g (u) Show that the systems Ax g below ıs consistent 지-2x2 + 3x3-2x4 (u) Fınd a linearly independent solution vector in part (b) (n) (c) Let A be any n x n and let P be any nonsngular n x n matrix AP) Prove that tr(A)tr(P (d) Show that if A is a square matrnx, then () (A A) is symmetric, (n) (A - A) is skew symmetric Hint A square matrix H is skew symmetric f H =-H

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