1 Quiz 2, Solution

Question 1

3x1x2+x3= 1; x1=1

3x21

3x3+1

3

3x1+ 6x2+ 2x3= 0; x2=1

2x11

3x3

3x1+ 3x2+ 7x3= 4; x3=4

73

7x23

7x1

x(0) =x(0)

1; x(0)

2; x(0)

3t

= (0;0;0)t

x1=1

3x21

3x3+1

3x2=0;x3=0 =x1= 0:333 33

x2=1

2x11

3x3x1=0:333 33;x3=0 =x2=0:166 67

x3=4

73

7x23

7x1x1=0:333 33;x2=0:166 67 =x3= 0:5

x(1) =x(1)

1; x(1)

2; x(1)

3t

= (0:333 33;0:166 67;0:5)t

x1=1

3x21

3x3+1

3x2=0:166 67;x3=0:5=x1= 0:111 11

x2=1

2x11

3x3x1=0:111 11;x3=0:5=x2=0:222 22

x3=4

73

7x23

7x1x1=0:111 11;x2=0:222 22 =x3= 0:619 05

x(2) =x(2)

1; x(2)

2; x(2)

3t

= (0:111 11;0:222 22;0:61905)t

max (j0:111 11 0:333 33j;j0:222 22 + 0:166 67j;j0:619 05 0:5j) = 0:222 22

x(2) x(1)

1

x(2)

1

=max (j0:11111 0:33333j;j0:22222 + 0:16667j;j0:61905 0:5j)

max (0:52381;0:222 22;0:52381) = 0:424 24

1

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Question 2

10x1x2= 9; x1=

1

10x2+9

10

x1+ 10x22x3= 7; x2=1

10x1+1

5x3+7

10

2x2+ 10x3= 6; x3=1

5x2+3

5

x(0) =x(0)

1; x(0)

2; x(0)

3t

= (0;0;0)t

x1=1

10 x2+9

10 x2=0;x3=0 =x1= 0:

x2=1

10 x1+1

5x3+7

10 x1=0:9;x3=0 =x2= 0:79

x3=1

5x2+3

5x1=0:9;x2=0:79 =x3= 0:758

x(1) =x(1)

1; x(1)

2; x(1)

3t

= (0:9;0:79;0:758)t

x1=1

10 x2+9

10 x2=0:79;x3=0:758 =x1= 0:979

x2=1

10 x1+1

5x3+7

10 x1=0:979;x3=0:758 =x2= 0:949 5

x3=1

5x2+3

5x1=0:979;x2=0:949 5 =x3=:789 9

x(2) =x(2)

1; x(2)

2; x(2)

3t

= (0:979 ;0:949 5;0:789 9)t

x(2) x(1)

1

x(2)

1

=max (j0:979 0:9j;j0:949 5 0:79j;j0:789 9 0:758j)

max (0:979;0:949 5;0:789 9) = 0:162 92

x(2) x(1)

1= max (j0:979 0:9j;j0:949 5 0:79j;j0:789 9 0:758j) = 0:159 5

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saripella

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University:
Biyani Girls College

Subject:
Numerical Analysis

Upload date:
31/07/2012