Quiz No.2 MTH603 Numerical Analysis Fall 2013 Due Date 17 December 2013

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Dear Students:
Your QUIZ 2 will be started on December 16, 2013 at 00:00 and will be closed on December 17, 2013 at 23:59. 
The quiz will be from Lecture No. 15 to Lecture No.19.
Before starting QUIZ, Please read the instructions carefully.
*   Quiz is based upon Multiple Choice Questions (MCQs).
    * You have to attempt the quiz online. You can start attempting the quiz any time within given date(s) of a  by clicking the link for Quiz in LMS.
    * The time to attempt the Quiz is limited. Once you login to attempt the quiz, the countdown will start and you have to complete the quiz in given amount of time. So always keep an eye on the remaining time.
    * Attempting quiz is unidirectional. Once you move forward to the next question, you can not go back to the previous one. Therefore before moving to the next question, make sure that you have selected the best option.
    * If for any reason, you lose access to internet (like power failure or disconnection of internet), you will be able to attempt the quiz again from the position where you left in last attempt. But remember that you have to complete the quiz before expiry of the deadline.
    * If any student failed to attempt the quiz in given time then no re-take or offline quiz will be held.

Best of Luck

[°ƻαɦɤα°]

Question # 1

Differences methods find the ________ solution of the system.

Select correct option:

Numerical

Analytical

 

Question # 2

 

The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue of A.

Select correct option:

TRUE

FALSE

 

 

Question # 3

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

Select correct option:

TRUE

FALSE

 

Question # 4

Eigenvalues of a _________ matrix are all real.

Select correct option:

Symmetric

Antisymmetric

Rectangular

triangular

 

Question # 5

By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.

Select correct option:

TRUE

FALSE

 

Question # 6

The dominant eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, smallest absolute value) of that matrix.

Select correct option:

TRUE

FALSE

  

Question # 7

Eigenvalues of a symmetric matrix are all _______ .

Select correct option:

Real

Complex

Zero

positive

 

 

Question # 8

Below are all the finite difference methods EXCEPT _________.

Select correct option:

jacobi’s method

newton's backward difference method

Stirlling formula

Forward difference method

 

Question # 9

The central difference method is finite method.

Select correct option:

True

False

Question # 10

Power method is applicable if the eigen vectors corresponding to eigen values are linearly _______.

Select correct option:

Independent

Dependent

 

Question #11

Central difference method seems to be giving a better approximation, however it requires more computations.

Select correct option:

TRUE

FALSE

 

Question #12

The Jacobi iteration ______, if A is strictly diagonally dominant

Select correct option:

Converges

Diverges

 

Question #13

Power method is applicable if the eigen values are ______________.

Select correct option:

real and distinct

real and equal

positive and distinct

negative and distinct

 

 

 

Question #14

determinant of a diagonal matrix is the product of the diagonal elements.

Select correct option:

TRUE

FALSE

 

Question #15

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

Select correct option:

same

different

 

Question #17

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to ______.

Select correct option:

Unity

Zero

 

 

  

[°ƻαɦɤα°]

Eigenvalues of a symmetric matrix are all _________. Real  Zero Question # 3 of 10 ( Start time: 05:52:09 PM ) Total Marks: 1  The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.  Select correct option:  TRUE FALSE Quiz Start Time: 05:49 PM Time Left 29  sec(s)  Question # 4 of 10 ( Start time: 05:53:07 PM ) Total Marks: 1  Central difference method seems to be giving a better approximation, however it requires more computations.  Select correct option:  TRUE FALSEQuiz Start Time: 05:49 PM Time Left 34  sec(s)  Question # 5 of 10 ( Start time: 05:54:29 PM ) Total Marks: 1  Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.  Select correct option:  TRUE FALSE Quiz Start Time: 05:49 PM Time Left 75  sec(s)  Question # 6 of 10 ( Start time: 05:55:50 PM ) Total Marks: 1  A 3 x 3 identity matrix have three and different eigen values.  Select correct option:  TRUE FALSE Quiz Start Time: 05:49 PM Time Left 68  sec(s)  Question # 7 of 10 ( Start time: 05:56:23 PM ) Total Marks: 1  Eigenvalues of a _________ matrix are all real.  Select correct option:  Symmetric Antisymmetric Rectangular triangular Quiz Start Time: 05:49 PM Time Left 87  sec(s)  Question # 9 of 10 ( Start time: 05:58:31 PM ) Total Marks: 1  For differences methods we require the initial approximation.  Select correct option:  TRUE FALSE Eigenvalues of a symmetric matrix are all _________. Real Zero Best of Luck

[sam]

its or today question?

[Naveed Abbas]

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 31
sec(s)

Question # 1 of 10 ( Start time: 09:38:10 PM ) Total Marks: 1

Two matrices with the same characteristic polynomial need not be similar.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 64
sec(s)

Question # 2 of 10 ( Start time: 09:39:22 PM ) Total Marks: 1

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 24
sec(s)

Question # 3 of 10 ( Start time: 09:40:41 PM ) Total Marks: 1

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

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 66
sec(s)

Question # 4 of 10 ( Start time: 09:42:00 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique
exists, consistent
trivial, unique
nontrivial, inconsistent

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 4
sec(s)

Question # 4 of 10 ( Start time: 09:42:00 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique
exists, consistent
trivial, unique
nontrivial, inconsistent

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 74
sec(s)

Question # 5 of 10 ( Start time: 09:43:34 PM ) Total Marks: 1

Central Difference method is the finite difference method.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 73
sec(s)

Question # 6 of 10 ( Start time: 09:44:38 PM ) Total Marks: 1

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 26
sec(s)

Question # 6 of 10 ( Start time: 09:44:38 PM ) Total Marks: 1

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE
FALSE Ans

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 69
sec(s)

Question # 7 of 10 ( Start time: 09:45:57 PM ) Total Marks: 1

A 3 x 3 identity matrix have three and different eigen values.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 6
sec(s)

Question # 7 of 10 ( Start time: 09:45:57 PM ) Total Marks: 1

A 3 x 3 identity matrix have three and different eigen values.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 33
sec(s)

Question # 8 of 10 ( Start time: 09:47:25 PM ) Total Marks: 1

The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of matrix A

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 68
sec(s)

Question # 9 of 10 ( Start time: 09:48:32 PM ) Total Marks: 1

Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero vector v such that _______.

Select correct option:

Av = xv
Ax = xv
Av + xv=0
Av = Ax

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 18
sec(s)

Question # 9 of 10 ( Start time: 09:48:32 PM ) Total Marks: 1

Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero vector v such that _______.

Select correct option:

Av = xv
Ax = xv
Av + xv=0
Av = Ax

http://quiz.vu.edu.pk/QuizQuestion.aspx?ver=bf207443-1fa9-415b-a850...

[pinky]

solved quiz

[Naveed Abbas]

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 31
sec(s)

Question # 1 of 10 ( Start time: 09:38:10 PM ) Total Marks: 1

Two matrices with the same characteristic polynomial need not be similar.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 64
sec(s)

Question # 2 of 10 ( Start time: 09:39:22 PM ) Total Marks: 1

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 24
sec(s)

Question # 3 of 10 ( Start time: 09:40:41 PM ) Total Marks: 1

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

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 66
sec(s)

Question # 4 of 10 ( Start time: 09:42:00 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique
exists, consistent
trivial, unique
nontrivial, inconsistent

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 4
sec(s)

Question # 4 of 10 ( Start time: 09:42:00 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique
exists, consistent
trivial, unique
nontrivial, inconsistent

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 74
sec(s)

Question # 5 of 10 ( Start time: 09:43:34 PM ) Total Marks: 1

Central Difference method is the finite difference method.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 73
sec(s)

Question # 6 of 10 ( Start time: 09:44:38 PM ) Total Marks: 1

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 26
sec(s)

Question # 6 of 10 ( Start time: 09:44:38 PM ) Total Marks: 1

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE
FALSE Ans

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 69
sec(s)

Question # 7 of 10 ( Start time: 09:45:57 PM ) Total Marks: 1

A 3 x 3 identity matrix have three and different eigen values.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 6
sec(s)

Question # 7 of 10 ( Start time: 09:45:57 PM ) Total Marks: 1

A 3 x 3 identity matrix have three and different eigen values.

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 33
sec(s)

Question # 8 of 10 ( Start time: 09:47:25 PM ) Total Marks: 1

The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of matrix A

Select correct option:

TRUE
FALSE

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 68
sec(s)

Question # 9 of 10 ( Start time: 09:48:32 PM ) Total Marks: 1

Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero vector v such that _______.

Select correct option:

Av = xv
Ax = xv
Av + xv=0
Av = Ax

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 18
sec(s)

Question # 9 of 10 ( Start time: 09:48:32 PM ) Total Marks: 1

Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero vector v such that _______.

Select correct option:

Av = xv
Ax = xv
Av + xv=0
Av = Ax

http://quiz.vu.edu.pk/QuizQuestion.aspx?ver=bf207443-1fa9-415b-a850...

BC090200783 : Wafiullah

Quiz Start Time: 09:38 PM
Time Left 35
sec(s)

Question # 10 of 10 ( Start time: 09:50:06 PM ) Total Marks: 1

The Jacobi iteration converges, if A is strictly diagonally dominant.

Select correct option:

TRUE Ans
FALSE

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 53
sec(s)

Question # 1 of 10 ( Start time: 10:01:34 PM ) Total Marks: 1

Jacobi’s method is highly recommended for ………… matrix to compute all the Eigen values and the corresponding eigenvectors.

Select correct option:

real symmetric
non real symmetric
real un-symmetric
None of the given choices

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 81
sec(s)

Question # 2 of 10 ( Start time: 10:02:14 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique
exists, consistent
trivial, unique
nontrivial, inconsistent

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 59
sec(s)

Question # 3 of 10 ( Start time: 10:02:33 PM ) Total Marks: 1

The determinant of a _______ matrix is the product of the diagonal elements.

Select correct option:

diagonal
upper triangular
lower triangular
scalar

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 66
sec(s)

Question # 4 of 10 ( Start time: 10:03:38 PM ) Total Marks: 1

A and its transpose matrix have _______ eigenvalues.

Select correct option:

same
different

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 83
sec(s)

Question # 5 of 10 ( Start time: 10:04:45 PM ) Total Marks: 1

The Jacobi iteration ______, if A is strictly diagonally dominant.

Select correct option:

converges
diverges

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 72
sec(s)

Question # 6 of 10 ( Start time: 10:05:40 PM ) Total Marks: 1

Differences methods are iterative methods.

Select correct option:

TRUE
FALSE

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 66
sec(s)

Question # 7 of 10 ( Start time: 10:07:21 PM ) Total Marks: 1

The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

Select correct option:

TRUE
FALSE

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 73
sec(s)

Question # 8 of 10 ( Start time: 10:08:22 PM ) Total Marks: 1

For differences methods we require the set of values.

Select correct option:

TRUE
FALSE

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 49
sec(s)

Question # 9 of 10 ( Start time: 10:09:09 PM ) Total Marks: 1

Numerical solution of 2/3 up to four decimal places is ________.

Select correct option:

0.667
0.6666
0.6667
0.66667

BC090200044 : Naveed Abbas

Quiz Start Time: 10:01 PM
Time Left 70
sec(s)

Question # 10 of 10 ( Start time: 10:10:07 PM ) Total Marks: 1

The dominant eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, smallest absolute value) of that matrix.

Select correct option:

TRUE
FALSE

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 7
sec(s)

Question # 1 of 10 ( Start time: 10:15:19 PM ) Total Marks: 1

The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue of A.

Select correct option:

TRUE
FALSE

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 84
sec(s)

Question # 2 of 10 ( Start time: 10:16:50 PM ) Total Marks: 1

Numerical solution of 2/3 up to four decimal places is ________.

Select correct option:

0.667
0.6666
0.6667
0.66667

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 80
sec(s)

Question # 3 of 10 ( Start time: 10:17:08 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.

Select correct option:

TRUE
FALSE

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 81
sec(s)

Question # 4 of 10 ( Start time: 10:17:27 PM ) Total Marks: 1

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

Select correct option:

TRUE
FALSE

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 38
sec(s)

Question # 5 of 10 ( Start time: 10:17:46 PM ) Total Marks: 1

In Jacobi’s Method, the rate of convergence is quite slow compared with other methods.

Select correct option:

TRUE
FALSE

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 84
sec(s)

Question # 6 of 10 ( Start time: 10:18:48 PM ) Total Marks: 1

The Jacobi iteration ______, if A is strictly diagonally dominant.

Select correct option:

converges
diverges

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 84
sec(s)

Question # 7 of 10 ( Start time: 10:19:01 PM ) Total Marks: 1

The determinant of a _______ matrix is the product of the diagonal elements.

Select correct option:

diagonal
upper triangular
lower triangular
scalar

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 53
sec(s)

Question # 8 of 10 ( Start time: 10:19:15 PM ) Total Marks: 1

Eigenvalues of a symmetric matrix are all _______ .

Select correct option:

real
complex
zero
positive

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 66
sec(s)

Question # 9 of 10 ( Start time: 10:20:01 PM ) Total Marks: 1

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE
FALSE Ans not confirem plz confirmed it

BS100200863 : Muhammad Rehan

Quiz Start Time: 10:15 PM
Time Left 67
sec(s)

Question # 10 of 10 ( Start time: 10:21:13 PM ) Total Marks: 1

Below are all the finite difference methods EXCEPT _________.

Select correct option:

jacobi’s method
newton's backward difference method
Stirlling formula Ans not sure
Forward difference method