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extra - matrix M = ± A B C D ² is composed of n × n...

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Linear Algebra Extra Credit Problems May 31, 2006 The following problems may be done for extra credit on the first exam. Nor- mally I encourage everyone to work together on homeworks but since this is for extra credit I’d prefer if you work on your own. This also means that the solutions should be your own, without looking at books, articles, etc. Do whatever you can and hand in what you have by the first exam. 1. Suppose a 2 n ×
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Unformatted text preview: matrix M = ± A B C D ² is composed of n × n blocks A,B,C,D . It is NOT in general the case that det M = det( AD-CB ). (2 points) Find an example when det M 6 = det( AD-CB ) (3 points) Show that if A is nonsingular and AC = CA then the formula holds. 2. (2 points) Show that det 1 1 1 a b c a 2 b 2 c 2 = ( b-a )( c-a )( c-b ). (3 points) Find and show a similar formula for n × n matrices. 1...
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