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e309k - MAS 3105 Quiz III and Key Prof S Hudson 1[15pt...

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MAS 3105 May 21, 2009 Quiz III and Key Prof. S. Hudson 1) [15pt] Apply the elimination method to compute det A (apply GE to simplify it, perhaps to triangular form, and then ask yourself if/how that affected the det): A = 0 3 1 1 1 1 1 3 0 0 2 2 - 1 - 1 - 1 2 2) [5pt] How do you tell MATLAB to create a random 5x5 matrix ? (show me what you’d type onto the command line). 3) [20pt] True-False. You can assume all the matrices are square here, and in problem 4 below. The set S = { [ x 1 , x 2 ] T : x 1 + x 2 = 10 } is a subspace of R 2 . The set of symmetric 2x2 matrices is a subspace of R 2 x 2 . det( A k ) = (det A ) k If A and B are row equivalent, then they have the same determinant. If A is singular, then A adj ( A ) = O (the zero matrix). 4) [20pt] Prove ONE: You can answer on the back. a) Prove that if A is singular then adj( A ) is also singular. b) Suppose A and B are both nxn. Prove that if AB = I , then BA = I . Do not assume A is nonsingular (it might be true, but you’ll have to prove it, if you want to use it).
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