e211k - formula for the transpose of A-1 , you can use it...

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MAS 3105 Feb 3, 2011 Quiz II and Key Prof. S. Hudson 1) [15pt] Use an inverse matrix to find the 2 × 2 matrix X such that BX = C , given that B = ± 0 1 1 3 ² C = ± 0 2 0 1 ² 2) [10pt] What is the MATLAB notation for A T ? [if you are using other software, explain, and answer for your software (at your own risk)]. 3) [20pt] True-False. You can assume all the matrices are square here, and in problem 4 below. There is an elementary matrix E such that det E = 0. If x = (1 , 2 , 3) T is a solution of the square system A x = 0 , then det A = 0. For every square matrix, 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) [15pt] Prove ONE: You can answer on the back. a) If A is a symmetric nonsingular matrix, then A - 1 is also symmetric [if you know a
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Unformatted text preview: formula for the transpose of A-1 , you can use it without proving it]. b) Prove this part of the TFAE theorem: If A is row equivalent to I , then A is nonsingular. c) If A is nonsingular, prove that det( A ) 6 = 0 [part of a Ch 2.2 theorem]. Remarks and Answers: I gave people a small break on the MATLAB problem, since the lab access has been difficult; if you missed that one, I reduced the problem to 5 points and raised the TF problem to 25. The overall average was 45/60. The unofficial scale is: A’s: 51 to 60 B’s: 45 to 50 C’s: 39 to 44 D’s: 33 to 38 F’s: 0 to 32 1) X = B-1 C = ±-5 2 ² 2) A 3) FTTFT 4) See text, or me. 1...
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This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

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