MTH603 Grand Quiz Solution and Discussion


Let[A]bea3×3realsymmetricmatrixwitha23bethenumericallylargestoff−diagonalelementthenusingJacobi′smethodthevalueofθcanbefoundby
Let A be a 3×3 matrix with real entries. Prove that if A is not similar over
R to a triangular matrix then A is similar over C to a diagonal matrix. 
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 ? 
Central Difference method is the finite difference method
Finite difference. A finite difference is a mathematical expression of the form f (x + b) − f (x + a). … The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.


Whileusingtherelaxationmethodforfindingthesolutionofthefollowingsystem11x1+x2−x3=8 x1+8x2+5x3=9 x1+x2+9x3=7withtheinitialvector(0,0,0),theresidualswouldbe

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

If the determinant of a matrix A is not equal to zero then the system of equations will have……….
A nxn nonhomogeneous system of linear equations has a unique nontrivial solution if and only if its determinant is nonzero. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.

For the system of equations; x =2, y=3. The inverse of the matrix associated with its coefficients is.

While using Jacobi method for the matrix
A=⎡⎣⎢⎢11/41/21/41/31/41/21/41/5⎤⎦⎥⎥the value of ‘theta θ’ can be found as

If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y =  4, then largest residual in 1st iteration will reduce to .

Whichofthefollowingisaforwarddifferencetableforthegivenvaluesofxandy?xy0.10.0030.50.1480.90.37

While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system;
2x+3y = 1, 3x +2y =  4 ? 
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?