<![CDATA[MTH603 Quiz 1 Solution and Discussion]]>Please share your Quiz

]]>https://community.secnto.com//topic/1203/mth603-quiz-1-solution-and-discussionRSS for NodeMon, 08 Jun 2026 19:04:39 GMTFri, 24 Jan 2020 17:23:38 GMT60<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 24 Jan 2020 17:25:38 GMT]]>To improve the accuracy of the derivative of the function, which of the following method is more helpful? MTH603

Extrapolation
Interpolation
Divided difference
Central difference

]]>https://community.secnto.com//post/3206https://community.secnto.com//post/3206Fri, 24 Jan 2020 17:25:38 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 06 Sep 2024 08:28:47 GMT]]>]]>https://community.secnto.com//post/7624https://community.secnto.com//post/7624Fri, 06 Sep 2024 08:28:47 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:35:52 GMT]]>how many eigenvalues will exit corresponding to the function exp(ax)

]]>https://community.secnto.com//post/7212https://community.secnto.com//post/7212Fri, 31 May 2024 14:35:52 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:35:29 GMT]]>for a function; y=f(x), if y0, y1 are 2,3

]]>https://community.secnto.com//post/7211https://community.secnto.com//post/7211Fri, 31 May 2024 14:35:29 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:35:12 GMT]]>Jacobian Method in Matrix Form
Let the n system of linear equations be Ax = b. Let us decompose matrix A into a diagonal component D and remainder R such that A = D + R. Iteratively the solution will be obtained using the below equation.

]]>https://community.secnto.com//post/7210https://community.secnto.com//post/7210Fri, 31 May 2024 14:35:12 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:34:48 GMT]]>b) The eigenvalues of a real symmetric matrix need not be positive. They can be positive, negative, or even zero, depending on the elements and the specific structure of the matrix.

]]>https://community.secnto.com//post/7209https://community.secnto.com//post/7209Fri, 31 May 2024 14:34:48 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:34:23 GMT]]>Two similar matrices have the same eigenvalues, even though they will usually have different eigenvectors. Said more precisely, if B = Ai’AJ. I and x is an eigenvector of A, then M’x is an eigenvector of B = M’AM. So, A1’x is an eigenvector for B, with eigenvalue ).

]]>https://community.secnto.com//post/7208https://community.secnto.com//post/7208Fri, 31 May 2024 14:34:23 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:34:06 GMT]]>an eigenvector v is said to be normalized if the coordinate of largest magnitude is equal to aero?

]]>https://community.secnto.com//post/7207https://community.secnto.com//post/7207Fri, 31 May 2024 14:34:06 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:33:50 GMT]]>Let A be an n × n matrix. Then λ = 0 is an eigenvalue of A if and only if there exists a non-zero vector v ∈ Rn such that Av = λv = 0. In other words, 0 is an eigenvalue of A if and only if the vector equation Ax = 0 has a non-zero solution x ∈ Rn.

]]>https://community.secnto.com//post/7206https://community.secnto.com//post/7206Fri, 31 May 2024 14:33:50 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:33:37 GMT]]>while using jacobi method fot the matrix A=[1 1/4 1/4 1/4 1/3 1/2 1/3 1/2 1/5]

]]>https://community.secnto.com//post/7205https://community.secnto.com//post/7205Fri, 31 May 2024 14:33:37 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:33:25 GMT]]>Using the Jacobi method find all the eigenvalues and the corresponding 2 eigenvectors of the matrix A = 2 1 2 Iterate till the oR- ~1 2 diagonal elements, in magnitude; are less than 0.0005
Using the Jacobi method find all the eigenvalues and the corresponding 2 eigenvectors of the matrix A = 2 1 2 Iterate till the oR- ~1 2 diagonal elements, in magnitude; are less than 0.0005

]]>https://community.secnto.com//post/7204https://community.secnto.com//post/7204Fri, 31 May 2024 14:33:25 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:32:52 GMT]]>@cyberian said in MTH603 Quiz 1 Solution and Discussion:

Here is a table of iterations. The actual vector U is horizontal written as entry 1 and 2, and the current approximation to the first eigenvalue is in the third column. The first(largest in absolute value) eigenvalue is negative, so the system needs a certain time to reduce oscillations:

U[1] U[2] eigenvalue
1 0 0
1 3 1
1 -9/7 7
1 -57/11 -11/7
1 -261/103 -103/11
1 -1353/419 -419/103
1 -6669/2287 -2287/419

in float reprecentation

U[1] U[2] eigenvalue
1.0000000 0 0
1.0000000 3.0000000 1.0000000
1.0000000 -1.2857143 7.0000000
1.0000000 -5.1818182 -1.5714286
1.0000000 -2.5339806 -9.3636364
1.0000000 -3.2291169 -4.0679612
1.0000000 -2.9160472 -5.4582339
1.0000000 -3.0347480 -4.8320944
1.0000000 -2.9862913 -5.0694960
1.0000000 -3.0055137 -4.9725827
1.0000000 -2.9977994 -5.0110274
1.0000000 -3.0008810 -4.9955987
]]>https://community.secnto.com//post/7203https://community.secnto.com//post/7203Fri, 31 May 2024 14:32:52 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:31:22 GMT]]>Here is a table of iterations. The actual vector U is horizontal written as entry 1 and 2, and the current approximation to the first eigenvalue is in the third column. The first(largest in absolute value) eigenvalue is negative, so the system needs a certain time to reduce oscillations:

U[1] U[2] eigenvalue
1 0 0
1 3 1
1 -9/7 7
1 -57/11 -11/7
1 -261/103 -103/11
1 -1353/419 -419/103
1 -6669/2287 -2287/419
]]>https://community.secnto.com//post/7202https://community.secnto.com//post/7202Fri, 31 May 2024 14:31:22 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:28:57 GMT]]>I’m slightly confused about how to use the power method and the steps to calculate an eigenvalue. - I understand that the power method is defined as U(x+1) = AU(x)/a(x) where “a” is the first component of U(x). I do not understand at all what “U” is. Are we picking any vector we want that minimizes the error? What would I do given the practice problem below?

Apply the power method to
132−4
1 2 3 −4

to obtain three approximations of the largest eigenvalue of A. What is the limiting vector u∞?

]]>https://community.secnto.com//post/7201https://community.secnto.com//post/7201Fri, 31 May 2024 14:28:57 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 31 May 2024 14:28:14 GMT]]>while using jacobi method for the matrix a=[2 0 0 02 1 0 1 2] o=pi/4

]]>https://community.secnto.com//post/7200https://community.secnto.com//post/7200Fri, 31 May 2024 14:28:14 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Fri, 10 May 2024 06:12:29 GMT]]>@anas-khan please post into relevant category

]]>https://community.secnto.com//post/7198https://community.secnto.com//post/7198Fri, 10 May 2024 06:12:29 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Tue, 07 May 2024 05:59:29 GMT]]>Please Madam Answer This question.
Total Marks 5
Starting Date Friday, May 03, 2024
Closing Date Wednesday, May 08, 2024
Status Open
Question Title Graded Discussion Board
Question Description
Graded Discussion Board for Elementary English (ENG001) will be open from May 3, 2024, to May 8, 2024.

Give your opinion on this statement in 200 to 250 words.

A good writer is an architect of imagination, constructing worlds with carefully chosen bricks of language. How far do you agree with this statement?

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Best of luck!

Team ENG001

]]>https://community.secnto.com//post/7197https://community.secnto.com//post/7197Tue, 07 May 2024 05:59:29 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Mon, 06 May 2024 11:29:42 GMT]]>if the relaxation method is applied on the system

]]>https://community.secnto.com//post/7196https://community.secnto.com//post/7196Mon, 06 May 2024 11:29:42 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Mon, 06 May 2024 11:29:28 GMT]]>Which of the following rearrangement make strictly diagonal dominant, the system of linear

]]>https://community.secnto.com//post/7195https://community.secnto.com//post/7195Mon, 06 May 2024 11:29:28 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Mon, 06 May 2024 11:28:39 GMT]]>Which of the following rearrangements make the system of linear equations strictly diagonally dominant: 39 + 2 = -2 62 + 4y + 11z = 1 5r - 23 - 22 = 9 Select one: 2v - 22 = 9 3y = 2 6z + 4y + M = 1 6r + 4y + M = 1 -8v + 2 = -2 51 - %0 - 22 = 0 61 - %v - 28 - 0 Av + M2 = 30 + 2 = -2 No need to rearrange as the system is already diagonally dominant.
Which of the following rearrangements make the system of linear equations strictly diagonally dominant:
39 + 2 = -2
62 + 4y + 11z = 1
5r - 23 - 22 = 9

Select one:
2v - 22 = 9
3y = 2
6z + 4y + M = 1
6r + 4y + M = 1
-8v + 2 = -2
51 - %0 - 22 = 0
61 - %v - 28 - 0 Av + M2 = 30 + 2 = -2

No need to rearrange as the system is already diagonally dominant.

]]>https://community.secnto.com//post/7194https://community.secnto.com//post/7194Mon, 06 May 2024 11:28:39 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Mon, 06 May 2024 11:27:54 GMT]]>@cyberian said in MTH603 Quiz 1 Solution and Discussion:

gauss seidel method also known as?

Gauss–Seidel method is an improved form of Jacobi method, also known as the successive displacement method. This method is named after Carl Friedrich Gauss (Apr.

]]>https://community.secnto.com//post/7193https://community.secnto.com//post/7193Mon, 06 May 2024 11:27:54 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Mon, 06 May 2024 11:27:34 GMT]]>gauss seidel method also known as?

]]>https://community.secnto.com//post/7192https://community.secnto.com//post/7192Mon, 06 May 2024 11:27:34 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Mon, 06 May 2024 11:27:03 GMT]]>In … method, the elements above and below the diagonal are simultaneously made zero.

]]>https://community.secnto.com//post/7191https://community.secnto.com//post/7191Mon, 06 May 2024 11:27:03 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Wed, 21 Jun 2023 06:15:24 GMT]]>@cyberian said in MTH603 Quiz 1 Solution and Discussion:

while using relaxation method, which of th folowing is the

2x+3y = 1, 3x +2y =4 ?
(1,4)

]]>https://community.secnto.com//post/7094https://community.secnto.com//post/7094Wed, 21 Jun 2023 06:15:24 GMT<![CDATA[Reply to MTH603 Quiz 1 Solution and Discussion on Wed, 21 Jun 2023 06:08:00 GMT]]>@cyberian said in MTH603 Quiz 1 Solution and Discussion:

the linear equation 2x-0y-2=0 has

c01fab1a-1b9b-4bff-b820-e89da0f3dd81-image.png

]]>https://community.secnto.com//post/7093https://community.secnto.com//post/7093Wed, 21 Jun 2023 06:08:00 GMT