MTH603 Grand Quiz Solution and Discussion

Let [A] be a 3x3 real symmetric matrix with
a12
be numerically the largest offdiagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as 
The number of significant digits in the number 608.030060 is:
9

For two matrices A and B, such that “A = Inverse of B”, then which of the following is true?

The 2nd row of the augmented matrix of the system of linear equations is:
2x+z=4
xy+z=3
y+z=5 
If a system of equations has a property that each of the equation possesses one large coefficient and the larger coefficients in the equations correspond to different unknowns in different equations, then which of the following iterative method id preferred to apply?

While solving by GaussSeidel method, which of the following is the first Iterative solution for the system; x2y =1, x+4y=4 ?
a) (1, 0.75)
b) (0.25,1)
c) (0,0)
d) (1,0.65) 
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.
Eigenvectors of a matrix corresponding to distinct eigenvalues are linearly independent. ▫. If λ is an eigenvalue of multiplicity k of an n × n matrix A, then the number of … power method converges to the smallest eigenvalue in absolute value of A. … v2, …, vn, and that λ1 is a simple eigenvalue with the largest magnitude, i.e.,.

While using the GaussSeidel Method for finding the solution of the system of equation, the following system
2x+y−3z=5
x+3y+2z=7
x+2y+z=3can be rewritten as

Two matrices with the _______ characteristic polynomial need not be similar.
same
differentTwo similar matrices have the same characteristic polynomial. The converse however is not true in general: two matrices with the same characteristic polynomial need not be similar.

Jacobi’s Method is a/an………………
Iterative method
Direct method 
Whileusingtherelaxationmethodforfindingthesolutionofthefollowingsystem8x1+3x2−2x3=5 4x1+7x2+2x3=9 3x1+5x2+9x3=2withtheinitialvector(0,0,0),theresidualswouldbe

Gauss  Jordan Method is similar to ……….
Gauss–Seidel method
Iteration’s method
Relaxation Method
Gaussian elimination method 
The first row of the augmented matrix of the system of linear equations is:
2x+z=4
xy+z=3
y+z=5The first row of the augmented matrix of the system of linear equations is:
2x+z=4
xy+z=3
y+z=5 
Choleskey’s reduction method is also called
Bisection method 
While using the GaussSeidel Method for finding the solution of the system of equation, the following system
2x+2y+z=3
x+3y+z=2
x+y+z=2
can be rewritten as 
While using the relaxation method for finding the solution of the below given system, which of the following increment will be introduced?
6x1−2x2+3x3=1
−2x1+7x2+2x3=5
x1+x2−5x3=−13