# MTH603 Grand Quiz Solution and Discussion

• Eigenvalues of a _________ matrix are all real.

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

If A is strictly row diagonally dominant, then the Jacobi iteration converges for any choice of the initial approximation x(0). However, the Jacobi iteration may converge for a matrix that is not strictly row diagonally dominant.

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

• The linear equation 2x+0y-2=0 has----- solution(s).

• Let[A]bea3×3realsymmetricmatrixwith|a23|bethenumericallylargestoff−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 non-trivial solution if and only if its determinant is non-zero. 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

1

3

1

4

87

1

33

1
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