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Unformatted text preview: 1-2 4 1-2 1 3) Choose ONE of these to prove. You can answer on the back. a) If A is a symmetric nonsingular matrix, then A-1 is also symmetric [if you know a formula for the transpose of A-1 , you can use it without proving it). b) If A , B and C are 3x3 matrices such that AB = C and B is singular, then C is also singular. c) If A is 3x3 and the system Ax = b has a unique solution, then A is nonsingular. (Do not assume that b = 0). Answer to a): [ A-1 ] T = [ A T ]-1 = A-1 (explain each step), so A-1 is symmetric. Parts b) and c) were HW and I think you can nd the answers on previous keys. 1...
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- Spring '09