Matrix Algebra Review Fall 2009

Matrix Algebra Review Fall 2009 - AAEC 5024 Fall 2009...

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AAEC 5024 D. B. Taylor Fall 2009 August 24, 2009 MATRIX ALGEBRA REVIEW * Due Date: Monday, August 31, 2009 (Hillier and Lieberman – Appendix 4 is a good reference as are various math-matrix algebra texts.) REVIEW OF BASIC MATRIX OPERATIONS 1. XY =− = [ ] 3, 1, 2 [0, 0, 4] A= 10 3 0- 2 1 -1 B = 211 -1 0 4 -3 03 1 0 Determine the answers to the following (note that XX T ' ): a. X+Y f. AB b. X-Y g. BA c. 2X-3Y h. AA d. X(Y') i. (A')B e. 3A-B j. A((B-A)') 2. Write the following system of equations in matrix notation: 5X 1 + 3X 2 + 7X 3 = -4 9X 1 + 1X 2 + 6X 3 = 18 7.2X 1 + 5X 3 = 5 3. Without solving for the values of X, do the following systems of equations have no solutions, one solution, or infinitely many solutions? Why? Where AX = b *This mathematical review will not be graded, but I will go over your answers. It is wroth your while to become familiar with matrix algebra through this exercise. As you will eventually realize, the simplex algorithm, which is
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Matrix Algebra Review Fall 2009 - AAEC 5024 Fall 2009...

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