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Mth 603 today quizz
in the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
Pi/3
Pi/6
Pi/2
Pi/4
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
main diagonal
last column
last row
If n x n matrices A and B are similar, then they have the _____ eigenvalues (with the same multiplicities
same
different
Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
t
f
Differences methods are iterative methods.
t
f
A 3 x 3 identity matrix have three and __________eigen values.
same
different
Power method is applicable if the eigen values are real and distinct.
t
f
The dominant or principal eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, largest absolute value) of that matrix.
t
f
If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
t
f
In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be ………… to the sum of the diagonal elements of the original matrix A
Greater than
less then
same
different
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in the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
Pi/3
Pi/6
Pi/2
Pi/4
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
main diagonal
last column
last row
If n x n matrices A and B are similar, then they have the _____ eigenvalues (with the same multiplicities
same
different
Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
t
f
Differences methods are iterative methods.
t
f
A 3 x 3 identity matrix have three and __________eigen values.
same
different
Power method is applicable if the eigen values are real and distinct.
t
f
The dominant or principal eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, largest absolute value) of that matrix.
t
f
If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
t
f
In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be ………… to the sum of the diagonal elements of the original matrix A
Greater than
less then
same
different
solution
Question # 1 of 10 ( Start time: 09:20:13 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
Question # 2 of 10 ( Start time: 09:20:42 PM ) Total Marks: 1
For a function; y=f(x), if y0, y1 and y2 are 2,3 and 5
respectively then which of the following will be 2nd order
Backward difference at y2 = 5 ?
Select correct option:
-1
-2
1
2
Question # 3 of 10 ( Start time: 09:21:12 PM ) Total Marks: 1
How many Eigen vectors will exist corresponding to the function;
Exp(ax) = e^ax, when the matrix operator is of differentiation?
Select correct option:
Infinite many
Unique
Finite Multiple
None
Question # 4 of 10 ( Start time: 09:21:33 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
Question # 5 of 10 ( Start time: 09:22:10 PM ) Total Marks: 1
Power method is applicable if the eigen values are real and
distinct.
Select correct option:
TRUE
FALSE
Question # 6 of 10 ( Start time: 09:22:28 PM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a
matrix that has ____ zeros along its main diagonal.
Select correct option:
no
atleast one
Question # 7 of 10 ( Start time: 09:22:43 PM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a
matrix that has no zeros along its main diagonal.
Select correct option:
TRUE
FALSE
Question # 8 of 10 ( Start time: 09:22:58 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
Question # 9 of 10 ( Start time: 09:23:09 PM ) 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
x^3-1
x^3+1
Question # 10 of 10 ( Start time: 09:23:57 PM ) Total
Marks: 1
The dominant or principal eigenvector of a matrix is an
eigenvector corresponding to the eigenvalue of largest magnitude
(for real numbers, largest absolute value) of that matrix.
Select correct option:
TRUE
FALSE
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