e203k - symmetric. b) If A , B and C are 3x3 matrices such...

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MAS 3105 Feb 4, 2003 Quiz II Key Prof. S. Hudson 1) Find an elementary matrix E so that EA = B . A = ± 1 1 2 0 ² B = ± 1 1 3 1 ² Ans: Row 2 of B = Row 1 of A + Row 1 of A . So, we apply the same operation to the 2x2 identity matrix and get E (which we should quickly check): E = ± 1 0 1 1 ² 2) Find the inverse of the matrix A by using Gaussian elimination on an augmented matrix. Check by multiplying out AA - 1 . A = 1 0 1 0 1 0 1 0 2 Ans : A - 1 = 2 0 - 1 0 1 0 - 1 0 1 3) Choose ONE of these to prove. You can answer on the back. a) If A and B are symmetric 3x3 matrices, and AB = BA , then AB is
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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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