MTH603 Numerical Analysis Assignment 01 Fall 2020 Solution / Discussion
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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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