MTH603 Grand Quiz Solution and Discussion

In GaussJacobi’s method, the corresponding elements of
x(r+1)i
replaces those of
x®i
as soon as they become available.True
False 
While using the GaussSeidel Method for finding the solution of the system of equation, the following system
x+2y+2z=3
x+3y+3z=2
x+y+5z=2can be rewritten as

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
If one root of the equation is37i, then the other root will be
37i
3+7i
37i
3+7i 
If one root of the equation is37i, then the other root will be
37i
3+7i
37i
3+7i 
@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
In Jacobi’s Method, We assume that the …………elements does not vanish.
Mathematical Methods for Numerical Analysis and Optimization … Solution of Linear System of Equationsand Matrix Inversion Jacobi’s Method This is an iterative … We also assume that the diagonal element do not vanish.

In Jacobi’s Method, We assume that the …………elements does not vanish.
Diagonal
Offdiagonal
Row
Column 
While using Jacobi method for the matrix
A=⎡⎣⎢⎢2−10−120002⎤⎦⎥⎥
and ‘theta θ =pi/4’, the orthogonal matrix S1 
@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
Gauss elimination and GaussJordan methods are popular among many methods for finding the ………of a matrix.

Gauss elimination and GaussJordan methods are popular among many methods for finding the ………of a matrix.
Identity
Transpose
Inverse
None of the given choices 
While using power method, the computed vector
u(2)=⎛⎝⎜⎜6.5714289.5714211.21423⎞⎠⎟⎟
will be in normalized form asWhile using power method, the computed vector [{u^{(2)}} = \left( {\begin{array}{*{20}{c}} {6.571428}\{9.57142}\{11.21423} \end{array}} \right)] will be in normalized form as

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
In GaussSeidel method, each equation of the system is solved for the unknown with  coefficient, in terms of remaining unknowns.
110 Solving each equation of the given system for the unknown with the largest coefficient in terms of the remaining unknowns, we have x = 37. Example 19. Solve the following system by Gauss–Seidel method : by Gauss–Seidel

In GaussSeidel method, each equation of the system is solved for the unknown with  coefficient, in terms of remaining unknowns.
smallest
largest
any positive
any negative 
@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
Let [A] be a 3x3 real symmetric matrix with
a12be numerically the largest offdiagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as
⎡⎣⎢⎢1000cosθsinθ0−cosθ−sinθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥ 
Let [A] be a 3x3 real symmetric matrix with
a12be numerically the largest offdiagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as
⎡⎣⎢⎢1000cosθsinθ0−cosθ−sinθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥ 
While using Relaxation method, which of the following is increment ‘dxi’corresponding to the largest Residual for 1st iteration on the system;
2x+3y = 1, 3x +2y =  4 ?4
3 REF
2
1 
@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.