Unformatted text preview: 12 4 12 1 3) Choose ONE of these to prove. You can answer on the back. a) If A is a symmetric nonsingular matrix, then A1 is also symmetric [if you know a formula for the transpose of A1 , 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): [ A1 ] T = [ A T ]1 = A1 (explain each step), so A1 is symmetric. Parts b) and c) were HW and I think you can ﬁnd the answers on previous keys. 1...
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 Spring '09
 JULIANEDWARDS
 Linear Algebra, Matrices, Invertible matrix, Transpose, Prof. S. Hudson

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