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 Quiz 1 Dear Students:Your QUIZ 1 has  started on December 02, 2013 at 00:00 and will be closed on December 03, 2013 at 23:59. The quiz will be from Lecture No. 9 to Lecture No.14.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.

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### Replies to This Discussion

Eigenvalues of a symmetric matrix are all _________.

real

zero

positive

negative

Question # 2 of 10 ( Start time: 10:23:07 AM )    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

Question # 3 of 10 ( Start time: 10:23:55 AM )    Total Marks: 1

Exact solution of 2/3 is not exists.

Select correct option:

TRUE

FALSE

Question # 4 of 10 ( Start time: 10:24:53 AM )    Total Marks: 1

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

Select correct option:

positive

negative

Question # 5 of 10 ( Start time: 10:26:04 AM )    Total Marks: 1

Differences methods find the ________ solution of the system.

Select correct option:

numerical

Analytical

Question # 6 of 10 ( Start time: 10:26:49 AM )    Total Marks: 1

The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

Select correct option:

(x-1)^3

x^3-1

x^3+1

Question # 7 of 10 ( Start time: 10:28:08 AM )    Total Marks: 1

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

Select correct option:

TRUE

FALSE

Question # 8 of 10 ( Start time: 10:29:33 AM )    Total Marks: 1

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

main diagonal

last column

last row

Question # 9 of 10 ( Start time: 10:30:33 AM )    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

Question # 10 of 10 ( Start time: 10:31:28 AM ) Total Marks: 1

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

Select correct option:

TRUE

FALSE

All eigenvalues of a real symmetric matrix are real.

So

Eigenvalues of a symmetric matrix are all _________.

real

zero

positive

negative

Properties of real symmetric matrices

nn                       T
Recall that a matrix A            is symmetric if A       A.
For real symmetric matrices we have the following two
crucial properties:
All eigenvalues of a real symmetric matrix are real.
Eigenvectors corresponding to distinct eigenvalues are
orthogonal.
To show these two properties, we need to consider
complex matrices of type A  nn , where  is the set of

complex numbers z  x  iy where x  and y  are the real
and imaginary part of z and i  1.

n
is the set of n-column vectors with components in
and similarly nn  is the set of n n matrices with complex

numbers as its entries.

We write the complex conjugate of z as z          x   iy. For
u  n  and A  nn , we denote by u   n  and
A   nn , their complex conjugates, obtained by taking

the complex conjugate of each of their components.

i think "A is inverse of B"

A is inverse of B

0

system may have infinite many solutions

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