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MTH603 Numerical Analysis Assignment 01 Fall 2020 Solution / Discussion

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MTH303 Assignment-3 Solution Fall 2020 | Virtual University

Mth603 Assignment No. 1

Fall 2020

Question No. 1:

Find the root of the equation x^3+x^2+x-1 =0 correct to two decimal places by using bisection method.

 

Solution:

F(1) is positive and f(0)is negative

Hence the root lies between is

 

F(0.5)  is negative and f(1) is positive

The root lies between 0.5&1

 

F(0.75) is positive and f(0.5) is negative

The root   lies between 0.75&0.5

F(0.625) is positive and f(0.5) is negative

The root lies between 0.625 &0.5

f(0.5625) is positive and f(0.5) is negative

The root lies between 0.5625&0.5

 

f(0.53125) is negative  and f(0.5625) is positive

The roort is lie between 0.53125&0.5625

F(0.5469) is negative and f(0.5469) is positive

The root is lie between 0.5469&0.53125

 

F(0.54) is negative and f(0.5469)

The root is lie between 0.54&0.5469

F(0.543) is negative and f(0.5469) is positive.

F(0.543) is negative and f(0.5449) is positive

The root lies between 0.543&0.5469

Hence approximate root ofgiven equation using bisection method is 0.54 correct up to two decimal.

 

 

Question No.2: 

Solve the system of linear equations with the help of Gaussian elimination method.

2x + y + z = 9;3x −2y + 4z = 9;x +y-2z = 3

 

Solution:

 

Put value of z in (2)

 

-y+5=3

-y=3-5

-y=-2

Y=2

Put y  ,z value in 1

X+2-2=3

X=3

Thus (x,y,z)=(3,2,1)

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