cont..
1.Given two nonsingular matrices A, B elements of Mn(R), show that
A^-1 – (A+B)^-1 = A^-1 (A^-1+ B^-1)^-1 A^-1
5. Definition. Let C element of Mn(R). C is said to be symmetric iff A=Atranspose. Given symmetric matrices A,B elements of Msubscript2(R), show that AB is also symmetric iff A,B commute with each other e.i. AB=BA.
6. If c is an associated eigenvalue of A element of Mn(R), show that c^k is an associated eigenvalue of A^k for some k element of N.
7. If A element of Mn(R) is a nilpotent matrix, show that the only eigenvalue of A is zero.
8. Let A, B elements of Mn(R) such that Ax=cx and Bx=bx. Show that
i.(A+B)x = (c+b)x
ii.(AB)x = (cb)x
2006-12-21
18:53:44
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4 answers
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Anonymous
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Mathematics