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

]]>Topics covered under playlist of Solution of System of Linear Simultaneous Equations:

Direct Method: Gauss Elimination Method, Gauss Jordan Method, Crout’s Method.

Indirect Method: Gauss Jacobi Method, Gauss Seidel Method, Relaxation Method.

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.

]]>@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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• Write your ID on the top of your solution file.

Don’t use colourful back grounds in your solution files.

Use Math Type or Equation Editor Etc. for mathematical symbols.

You should remember thatif we found the solution files of some students are same then we will reward zero marks to all those students.

Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero mark.

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

]]>Numerical Analysis.

Course Contents.

Solution of Non Linear Equations. ]]>

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.

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]]>Assallamulikum Sir, Conversion (59)10 into binary 59/2=28-1 ? 28/2=14-0 14/2=7-0 7/2=3-1 3/2=1-1 (111001) ?

Dear @Engr-Ali ,

$(59){10} = (111011){2}$

The mistake you have made is in the first step where you divided $59/2$. It has to be $29-1$ instead of $28-1$.

Best wishes

]]>What is synchronous and asynchronous and what are there applications in real world. Which applications use this sort of techniques.

The word synchronous and asynchronous are very general terms that are used in different fiels representing different phenonena. If you can please ask it more clearly that in what context you are asking. It will be good if you please mention what page of handouts, what slide of ppts or where in the lecture video of the numerical analysis you studied/heard about it. Then we’ll be able to explain it well.

Best wishes

]]>respected sir, sir ma na ye pochna tha ka regula falsi method ma hum ye bhi formula use kar sakta hai. please guide kar dya. the first approximation solution x1 is given by X1=(a(f(b))-b(f(a))/f(b)-f(a)

That is right. You can use this formula.

In fact, the formula given in the handouts becomes same after you simplify it. Also $x_{n-1}$ will become $a$ and $x_{n}$ will become $b$.

So use any from the two formulas you find easier.

Best wishes

]]>AoA, Sir if you may plz explain “replace the part of curve between the points A(x_n, f(x_n)) and B(x_n-1, f(x_n-1)) by a chord in the interval” . diagrammatic explanation will be a great help in comprehension of the subject matter. Thanks

A chord is basically a straight line by joining two points of a curve or circle. The root of a equation means that when we give input value x then the functional value of that input will be zero then x is called the root of that equation. We take the two points of the interval on the chord instead of the curve shape because the value of root lies in that interval and this mean this value will lie on x-axis and if this is the root then functional value will be zero and we know that y-axis (functional value) is zero at x-axis.

]]>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

0c7ad28d-7947-40be-9f9a-3f78480c6d1e-image.png

]]>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.

]]>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. ]]>

Spring 2020_MTH603_1_SOL.docx ]]>

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 ,