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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.
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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+1)^3          i m not sure about this answer

            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

            first row     i m not sure about this answer

 

 

 

 

 

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.

 reply ans

i think "A is inverse of B"

A is inverse of B

 

0

system may have infinite many solutions

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