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Unformatted text preview: symmetric. b) If A , B and C are 3x3 matrices such that AB = C and B is singular, then C is also singular. c) Prove that a square matrix A is singular if det( A ) = 0. Ans: These are HWs 1.3.25, 1.4.15 (see my Help pages) and part of Thm 2.2.2. Do not use Thm 2.2.3 in your answer, since it comes later in the course (avoid circular reasoning). For c), do not start by assuming A is singular; that is the other part of Thm 2.2.2 (the converse part). 1...
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 Spring '09
 JULIANEDWARDS

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