MTH603 Grand Quiz Solution and Discussion

Grand Quiz Total Questions : 30
Please read the following instructions carefully!
Quiz will be based upon Multiple Choice Questions (MCQs).You have to attempt the quiz online. You can start attempting the quiz any time within given date(s) of a particular subject by clicking the link for Quiz in VULMS.
Each question has a fixed time of 90 seconds. So you have to save your answer before 90 seconds. But due to unstable internet speeds, it is recommended that you should save your answer within 60 seconds. While attempting a question, keep an eye on the remaining time.
Attempting quiz is unidirectional. Once you move forward to the next question, you can not go back to the previous one. Therefore before moving to the next question, make sure that you have selected the best option.
DO NOT press Back Button / Backspace Button while attempting a question, otherwise you will lose that question.
DO NOT refresh the page unnecessarily, specially when following messages appear
Saving…
Question Timeout: Now loading next question…Javascript MUST be enabled in your browser; otherwise you will not be able to attempt the quiz.
If for any reason, you lose access to internet (like power failure or disconnection of internet), you will be able to attempt the quiz again from the question next to the last shown question. But remember that you have to complete the quiz before expiry of the deadline.
If any student failed to attempt the quiz in given time then no retake or offline quiz will be held.
Start Quiz


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