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# Lecture13 - Engineering Analysis ENG 3420 Fall 2009 Dan C...

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Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

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2 Lecture 13 Lecture 13 ± Last time: ² Problem solving in preparation for the quiz ² Linear Algebra Concepts ± Vector Spaces, Linear Independence ± Orthogonal Vectors, Bases ± Matrices ± Today ² Solving systems of linear equations (Chapter 9) ± Graphical methods ± Next Time ² Gauss elimination
Solving systems of linear equations ± Matrices provide a concise notation for representing and solving simultaneous linear equations: a 11 x 1 + a 12 x 2 + a 13 x 3 = b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 = b 2 a 31 x 1 + a 32 x 2 + a 33 x 3 = b 3 a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 x 1 x 2 x 3 = b 1 b 2 b 3 [ A ]{ x } = { b }

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Solving systems of linear equations in Matlab ± Two ways to solve systems of linear algebraic equations [A]{x}={b}: ² Left-division x = A\b ² Matrix inversion x = inv(A)*b ± Matrix inversion only works for square, non-singular systems; it is less efficient than left-division.
Solving graphically systems of linear equations ± For small sets of simultaneous equations, graphing them and determining the location of the intersection of the straight line representing each equation provides a solution . ± There is no guarantee that one can find the solution of system of linear equations: a) No solution exists b) Infinite solutions exist c) System is ill-conditioned

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Determinant of the square matrix A=[a ij ] ± Here the coefficient A ij of a ij is called the cofactor of A ± A cofactor is a polynomial in the remaining rows of A and can be described as the partial derivative of A. The cofactor polynomial
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Lecture13 - Engineering Analysis ENG 3420 Fall 2009 Dan C...

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