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Unformatted text preview: A = 3 232 , and you can easily check that A 2 = A . case 3 Suppose that c 6 = 0. (Note that there is overlap between cases 2 and 3.) Then, proceeding as in case 2, we are led to the matrices a ( aa 2 ) /c c 1a , where a is any number and c is any non zero number. 3.17 Does there exist an invertible 2 2 matrix A such that A 2 = 0. If so, nd an example. Otherwise, explain why not. SOLUTION No. Suppose that A is invertible, and let B be the inverse of A , so that BA = I . Then B 2 A 2 = BBAA = B ( BA ) A = BA = I . But if A 2 = 0, B 2 A 2 = 0. Since B 2 A 2 cannot equal both I and 0, there is no invertible matrix A with A 2 = 0. 21 /september/ 2005; 22:09 24...
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.
 Fall '08
 Gladue
 Calculus, Matrices

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