ES240_Chpt9

# ES240_Chpt9 - ES 240 Scientific and Engineering Computation...

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Unformatted text preview: ES 240: Scientific and Engineering Computation. Chapter 9: Gaussian Elimination Uchechukwu Ofoegbu Temple University Chapter 9: Gaussian Elimination ES 240: Scientific and Engineering Computation. Chapter 9: Gaussian Elimination Graphical Method Graphical Method ¡ The solution of a small set of simultaneous equations, can be obtained by graphing them and determining the location of the intercept ES 240: Scientific and Engineering Computation. Chapter 9: Gaussian Elimination Graphical Method (cont) Graphical Method (cont) ¡ Graphing the equations can also show systems where: a) No solution exists – The coefficient matrix is singular (determinant = 0) b) Infinite solutions exist – The coefficient matrix is singular (determinant = 0) c) System is ill-conditioned – The coefficient matrix is almost singular (determinant ≈ 0) ES 240: Scientific and Engineering Computation. Chapter 9: Gaussian Elimination Determinants Determinants ¡ The determinant D =| A | of a matrix is formed from the coefficients of [A]. ¡ Determinants for small matrices are: ¡ Determinants for matrices larger than 3 x 3 can be very complicated. 1 × 1 a 11 = a 11 2 × 2 a 11 a 12 a 21 a 22 = a 11 a 22 − a 12 a 21 3 × 3 a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 = a 11 a 22 a 23 a 32 a 33 − a 12 a 21 a 23 a 31 a 33 + a 13 a 21 a 22 a 31 a 32 ES 240: Scientific and Engineering Computation.ES 240: Scientific and Engineering Computation....
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ES240_Chpt9 - ES 240 Scientific and Engineering Computation...

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