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Unformatted text preview: A , B and C are 4 4 matrices with C = ( B T ) 2 . Further, given that det( A ) = 2 and det( B ) = 3. Find det(3 A-3 B 2 C-2 ). (5+5=10 points) Part II Solutions to problems here MUST BE WRITTEN IN DETAIL. You need not reprove theorems that I stated as such. However, if you use something from a problem that you have worked out before, you need to show those steps as well. 4. Do there exist invertible 3 3 matrices X and Y such that XY X-1 Y-1 = 1 0 2 0 2 1 0 0 1 ? Justify your answer rigorously. Hint: Think whether I have done a problem in class that is ideologically similar. ... (10 points) 5. Let A be an n n matrix. Show that the coecient of x n-1 in det( xI-A ) is equal to-Tr( A ). (10 points). 6. Find 2010 pairwise distinct 2 2 matrices A such that A 2010 = 1 0 0 1 . Hint: The key to this could lie with some geometry that we discussed. ...(10 points) 2...
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- Spring '08