ee231_ass7_sol

# ee231_ass7_sol - EE 231_B1 Numerical Analysis for...

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EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov - 1 - Solutions to Assignment 7 11.3 The following solution is generated with MATLAB. (a) >> A = [15 -3 -1;-3 18 -6;-4 -1 12]; >> format long >> AI = inv(A) AI = 0.07253886010363 0.01278065630397 0.01243523316062 0.02072538860104 0.06079447322971 0.03212435233161 0.02590673575130 0.00932642487047 0.09015544041451 (b) >> b = [3800 1200 2350]'; >> format short >> c = AI*b c = 320.2073 227.2021 321.5026 (c) The impact of a load to reactor 3 on the concentration of reactor 1 is specified by the element 1 13 a = 0.0124352. Therefore, the increase in the mass input to reactor 3 needed to induce a 10 g/m 3 rise in the concentration of reactor 1 can be computed as (d) The decrease in the concentration of the third reactor will be 11.9 (a) The matrix to be evaluated is 16 4 1 421 49 7 1 ⎡⎤ ⎢⎥ ⎣⎦ The row-sum norm of this matrix is 49 + 7 + 1 = 57. The inverse is 0.1667 0.1 0.0667 1.5 1.1 0.4 2.3333 2.8 0.5333 −−

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EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov - 2 - The row-sum norm of the inverse is ۖ -2.3333 ۖ + 2.8 + 0.5333 = 5.6667. Therefore, the condition number is Cond[ A ] = 57(5.6667) = 323 This can be verified with MATLAB,
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ee231_ass7_sol - EE 231_B1 Numerical Analysis for...

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