PYQs

1) Explain the main steps of the Gauss-Jordan method and apply this method to find the inverse of the matrix [266286268].

[2017, 10M]

2) Find the values of the two-valued variables A, B, C and D by solving the set of simultaneous equations A′+A.B=0A.B=A.CA.B+A.C′+C.D=C′.D.

[2001, 15M]

1) Apply Gauss-Seidel iteration method to solve the following system of equation:
2x+y−2z=17
3x+20y−z=−18
2x−3y+20z=25, correct to three decimal places.

[2019, 15M]

2) Find the solution of the system
10x1−2x2−x3−x4=3
−2x1+10x2−x3−x4=15 −x1−x2+10x3−2x4=27
−x1−x2−2x3+10x4=−9
using Gauss-Seidel method (make four iterations).

[2015, 15M]

3) Solve the system of equations 2x1−x2=7
−x1+2x2−x3=1
−x2+2x3=1
using Gauss-Seidel iteration method (perform three iterations).

[2014, 15M]

4) Solve the following system of simultaneous equations, using Gauss-Seidel iterative method:

3x+20y−z=−18
20x+y−2z=17
2x−3y+20z=25

[2012, 20M]

5) Given the system of equations:

2x+3y=1
2x+4y+z=2
2x+6z+Aw=4
4z+Bw=C

State the solvability and uniqueness conditions for the system. Give the solution when it exists.

[2010, 20M]

6) The equation x2+ax+b=0 has two real roots α and β. Show that the iterative method given by: xk+1=−(axk+b)xk, k=0,1,2… is convergent near x=α, if |α|>|β|.

[2009, 6M]

7) Apply Gauss-Seidel method to calculate x, y, z from the system:
−x−y+6z=42
6x−y−z=11.33
−x+6y−z=32
with initial values (4.67, 7.62, 9.05). Carry out computations for two iterations.

[2008, 15M]

8) Using Gauss-Seidel iterative method, find the solution of the following system:
4x−y+8z=26 5x+2y−z=6 x−10y+2z=−13
up to three iterations.

[2004, 15M]

9) Using Gauss Seidel iterative method and the starting solution x1=x2=0, determine the solution of the following system of equations in two iterations:
10x1−x2−x3=8
x1+10x2+x3=12
x1−x2+10x3=10

Compare the approximate solution with the exact solution.

[2001, 30M]