Page 159 - Numerical Analysis Using MATLAB and Excel

Solutions to End−of−Chapter Exercises

–
Multiplication of (1) by 3 yields
– 3x + 6x – 3x = 12 (6)
1
2
3
Addition of (3) and (6) yields
10x – 8x = 12 (7)
3
2
Multiplication of (5) by 10 yields
– 10x + 30x = 10 (8)
2
3
Addition of (7) and (8) yields
22x = 22 (9)
3
or
x = 1 (10)
3
Substitution of (10) into (7) yields
10x – 8 = 12 (11)
2
or
x = 2 (12)
2
and substitution of (10) and (12) into (1) yields

x – 4 + 1 = – 4 (13)
1
or
x = – 1 (14)
1
6.

Delta=[−1 2 −3 5; 1 3 2 −1; 3 −3 2 4; 4 2 5 1];
D1=[14 2 −3 5; 9 3 2 −1; 19 −3 2 4; 27 2 5 1];
D2=[−1 14 −3 5; 1 9 2 −1; 3 19 2 4; 4 27 5 1];

D3=[−1 2 14 5; 1 3 9 −1; 3 −3 19 4; 4 2 27 1];
D4=[−1 2 −3 14; 1 3 2 9; 3 −3 2 19; 4 2 5 27];

x1=det(D1)/det(Delta), x2=det(D2)/det(Delta),...
x3=det(D3)/det(Delta), x4=det(D4)/det(Delta)
x1=1 x2=2 x3=3 x4=4

Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−41
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