mth603 solved mcq's for midterm fall 2010 december 1

[Xpert]

Exact solution of 2/3 is not exists.
TRUE
FALSE

The Jacobi’s method is
a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

no
atleast one


A 3 x 3 identity matrix have three and __________eigen values.
same
different


Eigenvalues of a symmetric matrix are all _______ .
real
complex
zero
positive

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

Below are all the finite difference methods EXCEPT _________.

jacobi’s method
newton's backward difference method
Stirlling formula
Forward difference method

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


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

TRUE
FALSE

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.

(x-1)^3
(x+1)^3
x^3-1
x^3+1


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

TRUE
FALSE


Question # 1 of 10 ( Start time: 10:22:24 AM ) Total Marks: 1

Eigenvalues of a symmetric matrix are all _________.
Select correct option:

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 eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue 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