Solve the system of equations
by using the Gauss Jacboi and Gauss Seidel method. The exact solution of the system is
Perform the required number of iterations so that the same accuracy is obtained by both the methods. What conclusions can you draw from the results obtained?
Solve the following linear system Ax = b of equations with partial pivoting
Store the multipliers and also write the pivoting vectors.
See Answer →Find the inverse of the matrix using Gauss Jordan Method.
Using x o= 0 find an approximation to one of the zeros of x³-4x+1=0 by using Birge-Vieta Method. Perform two iterations.
See Answer →Find an approximate value of the positive real root of xe x= 1 using graphical method. Use this value to find the positive real root of xex = 1 correct to three decimal places by fixed point iteration method.
See Answer →Using Maclaurin’s expansion for sin x , find the approximate value of 4 sin with the error bound 5 10 -5
Find an appropriate root of with 10-5 accuracy by
i) Newton Raphson Method
ii) Secant Method
What conclusions can you draw from here about the two methods?
See Answer →The equation has a positive root in the interval ]1, 2[. Write a fixed point iteration method and show that it converges. Starting with initial approximation x = 1.5 find the root of the equation correct to three decimal places.
Find the Boolean expression in the DNF form for the function defined in tabular form below:
| x | y | z | |
| 1 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 |
Is there a 4-regular graph on 7 vertices? Justify your answer.
See Answer →Solve the recurrence relation:
using generating function technique. Also find 5 a using your answer.
See Answer →How many numbers from 0 to 759 are not divisible by either 3 or 7?
See Answer →Define vertex connectivity and cut vertex set of any graph G. Find the vertex connectivity and cut vertex set for the following graph:
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A box contains 6 red and 4 green balls. Four balls are selected from the box at random. What is the probability that two of the selected balls will be red and two will be green?
See Answer →Show that if 7 colours are used to paint 50 bicycles and each bicycle is coloured with a single colour, at least 8 bicycles will have the same colour.
See Answer → is Hamiltonian, how are m and n related? Justify your answer
Find a recurrence relation for an , the number of ways to arrange cars in a row with n spaces if we can use Maruti 800, Tata Safari or Scorpio. A Tata Safari or Scorpio requires two spaces, whereas a Maruti 800 requires just one space. Assume that you have unlimited number of each type of car and we do not distinguish between 2 cars of the same type.
See Answer →Express 5 x in terms of falling factorials and hence evaluate m S5 for m = 0,1,2,3,4,5.
See Answer →write down and count all the partitions of the number 7. To verify your answer use the generating function for , Pn taking n= 7 in Theorem 5 (of Unit 5, Block2).
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