MTH603 Assignment 1 Solution and Discussion


  • Cyberian's Gold

    Assignment NO. 1 MTH603 (Fall 2019)

    Maximum Marks: 20 Due Date: 24 -11-2019

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    Question #1: Find the root of the equation, Perform three iteration of the equation,
    ln (x −1) + sinx = 0 by using Newton Raphson method.
    Question #2: Solve the system of linear equations with the help of Gaussian elimination method.
    x + y + z = 6; 2x − y + z = 3; x + z = 4


  • Cyberian's Gold

    Assignment No: 01
    Question #1: Find the root of the equation, Perform three iteration of the equation,
    ln (x −1) + sinx =0 by using Newton Raphson method.

    Ans: Let f(x) = ln(x+1) + sinx = 0 and f(x) = 1/(x-1) + cosx

    F (1.5) = ln(0.5) + (1.5) = - 0.0667

    F(2) = ln(1) + sin(2) = 0.035

    Since f (1.5) f (2) < 0 so roots lies in interval [1.5, 2]

    Let x0 = 1.75 . x0 can be taken in the interval any real number [ 1.5 , 2 ], we let mid point

    of this interval .
    As we know Newton Raphson method is

    Xn+1 = xn – f ( xn ) / f(xn)
    First iteration
    X1 = x0 –f(x0) / f(x0) = 1.75 - f(1.75) / f(1.75)
    = 1.75 – (-0.2571 / 2.3329) = 1.8602
    Second iteration:
    X2 = x1 - f(x) / f(x) = 1.8602 –[ f(1.8602) / f(1.8602)]
    = 1.8602 - ( -0.1181 / 2.1620 ) = 1.9148
    Third iteration:
    X3 = x2- f(x2) / f(x2) = 1.9148 –f(1.9148) / f(1.9148)
    = 1.9148 – [-0.0556/2.0926]
    = 1.9414
    Question #2: Solve the system of linear equations with the help of Gaussian elimination method.
    x + y + z = 6;2x − y + z = 3;x + z = 4

    ANS: In Gaussian elimination method we convert the augmented matrix into reduce

    Echelon form therefore,

    Augmented matrix is

    R2- 2R1 , R3 – R1

    -1R2 , -1R3
    R23
    R3-3R2

    X + Y+ Z = 6 ;………………….(1)
    Y = 2,
    Z = 3
    Put into eq (1),
    we get X = 1 ,


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