Numerical Analysis.

Course Contents.

Solution of Non Linear Equations. ]]>

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]]>@zaasmi said in MTH603 Assignment 2 Solution and Discussion:

Assignment NO. 2 MTH603 (Spring 2021)

Maximum Marks: 20

Due Date: July 30, 2021DON’T MISS THESE: Important instructions before attempting the solution of this assignment:

• To solve this assignment, you should have good command over 23 - 30 lectures.

Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 23-30 lectures.

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Also remember that you are supposed to submit your assignment in Word format any other like scan images etc. will not be accepted and we will give zero mark corresponding to these assignments.Question 1:

x 1.5 2.0 2.5 3.0 3.5 4.0 f(x) 3.375 7.000 13.625 24.000 38.875 59.000

Find the first and second derivative of function f(x) at x=1.5 if:MARKS 10

Question 2:

Using Newton’s forward interpolation formula, find the value of function f(1.6) if:

x 1 1.4 1.8 2.2 f(x) 3.49 4.82 5.96 6.5MARKS 10

MTH603 Assignment 2 Solution Spring 2021-converted.docx MTH603 Assignment 2 Solution Spring 2021.pdf

]]>Question #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

System of Linear Equations entered :

[1] 2x + y + z = 9

[2] 3x - 2y + 4z = 9

[3] x + y - 2z = 3

Solve by Substitution :

// Solve equation [3] for the variable y

[3] y = -x + 2z + 3

// Plug this in for variable y in equation [1]

[1] 2x + (-x +2z+3) + z = 9

[1] x + 3z = 6

// Plug this in for variable y in equation [2]

[2] 3x - 2•(-x +2z+3) + 4z = 9

[2] 5x = 15

// Solve equation [2] for the variable x

[2] 5x = 15

[2] x = 3

// Plug this in for variable x in equation [1]

[1] (3) + 3z = 6

[1] 3z = 3

// Solve equation [1] for the variable z

[1] 3z = 3

[1] z = 1

// By now we know this much :

x = 3

y = -x+2z+3

z = 1

// Use the x and z values to solve for y

y = -(3)+2(1)+3 = 2

Solution :

{x,y,z} = {3,2,1}

Convert the decimal number 80 into its binary equivalent.

Question 2:

Convert the binary number 2 (11001100) to its decimal equivalent.

Question 3:

Find the relative error when 17 is considered upto four decimal places.

Question 4:

Find the interval in which atleast one root of the equation 3 2 xx x 2 10 lies.

Question 5:

Find the real root of the equation 4 x x 10 0 in the interval [1, 2] by bisection method upto

two iterations. ]]>

A series 16+8+4+2+1 is replaced by the series 16+8+4+2, then it is called

Each number in the sequence is half the value of the number receding it. So the common difference in the series is dividing by two.

16÷2=8

8÷2=4

4÷2=2

2÷2=1

1÷2=½

The answer is ½ or 0.5

When you keep dividing by two, you will notice an interesting pattern: the denominator continues to increase by two, while the numerator value remains the same. That’s fascinating because in natural, whole numbers the numbers in the series would decrease by two.

1/4 , 1/8 , 1/16 etc.

]]>While solving a system of linear equations by Gauss Jordon Method, after all the elementary row operations if there lefts also zeros on the main diagonal then which of the is true about the system?

The question asked that while solving a system of linear equations where ghost Children method, after all the elementary operations, if their lives are all widows on the main diagonal, then which of the following history in the system. So first we have to know about the Gaussian elimination method. So Gaussian elimination is the name of the matter. We used to perform the three types of metrics. Cooperation on an undocumented metrics coming from a linear system of equations in order to find the solutions for such a system. This technique is also cultural reduction and it conjures up two stages forward elimination and backs institutions. The forward elimination estates refers to the road except needed to simplify the metrics in questions into the chloroform such states has the proposed to demonstrate if the system of equations for trade in the metrics have a unique possible solutions infinitely many solutions or just no solutions at all, he found that the system has no solutions, then there is no reason to continue the reduction the magic through the next states. So according to the given a statement, the correct officer is an officer and a. That each system me how infinitely many solutions. Thank you This after applying all the elementary row operations on the system. If the main diagonal is still conjures of zeros, that means that the system may have infinitely many solar cells. Thank you

]]>Spring 2020_MTH603_1_SOL.docx ]]>

Euler’s Method numerically computes the approximate ________ of a function.

Euler’s method is a numerical tool for approximating values for solutions of differential equations.

]]>Mth603 ka koi student hai tu plz yeh question bta dy kis trha solve ho ga Given the following data x:1 2 5 y:1 4 10 Value of 1st order divided difference f[2 , 5] is

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]]>If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

True

False

Since similar matrices A and B have the same characteristic polynomial, they also have the same eigenvalues. If B = PAP−1 and v = 0 is an eigenvector of A (say Av = λv) then B(Pv) = PAP−1(Pv) = PA(P−1P)v = PAv = λPv. Thus Pv (which is non-zero since P is invertible) is an eigenvector for B with eigenvalue λ.

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