# SECTION 9.2# Example 1

eq1 := 2*x1+6*x2+8*x3 = 16;

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eq2 := 4*x1+15*x2+19*x3 = 38;

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eq3 := 2*x1 + 3*x3 = 6;

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solve({eq1,eq2,eq3},{x1,x2,x3});# Check the book's answer

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# This is the method used in the book:eq2-2*eq1;

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eq2 := %;

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eq3 - eq1;

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eq3 := %;

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eq1 - 2*eq2;

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eq1 := %;

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eq3 +2*eq2;

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eq3 := %;

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eq1 -2*eq3;

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eq1 := %;

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eq2 -3*eq3;

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eq2 := %;

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eq1;eq2;eq3;

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# Example 2eq1 := x1+2*x2+4*x3+x4 = 0;

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eq2 := -x1-2*x2-2*x3 = 1;

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eq3 := -2*x1-4*x2-8*x3+2*x4=4;

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eq4 := x1+4*x2+2*x3 = -3;

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solve({eq1,eq2,eq3,eq4},{x1,x2,x3,x4});# Check book's answer

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# This is the method used in the book:# First eliminate x1 from last 3 equations:eq2 := eq2 + eq1;

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eq3 := eq3 + 2*eq1;

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eq4 := eq4 - eq1;

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#Next, swap equations 2 and 4:temp := eq4;

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eq4 := eq2;

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eq2 := temp;

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eq1;eq2;eq3;eq4;

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# Eliminate x2 from all equations except the second:eq1 := eq1-eq2;

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#Switch equations 3 and 4:temp := eq4;

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eq4 := eq3;

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eq3 := temp;

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eq1;eq2;eq3;eq4;

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# Eliminate x3 from all equations except the third:eq1 := eq1 - 3*eq3;

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eq2 := eq2 + eq3;

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eq1;eq2;eq3;eq4;

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# Eliminate x4 from all equations except the fourth:eq1 := eq1 +1/4*eq4;

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eq3 := eq3 -1/4*eq4;

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eq1;eq2;eq3;eq4;

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# Example 3eq1 := 2*x1+4*x2+x3 = 8;

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eq2 := 2*x1 + 4*x2 = 6;

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eq3 := -4*x1-8*x2+x3 = -10;

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solve({eq1,eq2,eq3},{x1,x2,x3}); # Check book's answer

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# Book's method:eq2 := eq2 -eq1;

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eq3 := eq3 + 2*eq1;

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eq3 := eq3 + 3*eq2;

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eq1;eq2;eq3;

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eq1 := eq1 + eq2;

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eq1;eq2;eq3;

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x2 := s; x3 := 2;

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x1 := solve(eq1,x1);

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# Example 4x1 := 'x1'; x2 := 'x2'; x3 := 'x3'; x4 := 'x4';

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eq1 := x1 - x2 + 2*x3 + 2*x4 = 0;

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eq2 := 2*x1 - 2*x2 + 4*x3 + 3*x4 = 1;

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eq3 := 3*x1-3*x2+6*x3+9*x4 = -3;

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eq4 := 4*x1 - 4*x2 + 8*x3 + 8*x4 = 0;

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eq2 := eq2 - 2*eq1;

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eq3 := eq3 -3*eq1;

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eq4 := eq4-4*eq1;

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eq1;eq2;eq3;eq4;

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# Eliminate x4 from first and third equations:eq1 := eq1 + 2*eq2;

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eq3 := eq3 + 3*eq2;

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eq1;eq2;eq3;eq4;

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x2 := s; x3 := t; x4 := -1;

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x1 := solve(eq1,x1);

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