Chemical Engineering Hand Written_Notes_Part_47

Chemical Engineering Hand Written_Notes_Part_47 - 96 3....

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96 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES has the condition number of C ( A )=3 . 8131 e +016 . If we attempt to compute inverse of this matrix using MATLAB (which has arguably one of the best linear equations solvers) we get following result (5.59) A 1 =10 16 × 0 . 4504 0 . 9007 0 . 4504 0 . 9007 1 . 8014 0 . 9007 0 . 4504 0 . 9007 0 . 4504 w i thawarn ing : ’ Matrix is close to singular or badly scaled. Results may be inaccurate. ’ The di culties in computing inverse of this matrix are apparent if we further compute product A × A 1 , which yields (5.60) A × A 1 = 0 40 08 0 40 0 On the other hand, consider matrix (5.61) B =10 17 × 121 212 113 with eigen values (5.62) λ 1 =4 . 5616 × 10 17 ; λ 2 = 1 × 10 17 ; λ 3 =4 . 3845 × 10 18
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Chemical Engineering Hand Written_Notes_Part_47 - 96 3....

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