MTH603-Numerical Analysis Mid-Term Grand Quiz Fall 2021

 

MID-TERM GRAND QUIZ
 FALL 2020

Question No 1:

The characteristics polynomial of a 3 x 3 identity matrix is _______ if x is the (Raise For Success) Eigen values of given 3 x 3 identity matrix. Where symbol ^ shows power.

• (x-1)^3 Correct
• (x+1)^3
• X*3-1
• X^3+1

Question No 2:

In the relaxation method is applied on the system 2x+3y=1, 3x+2y=-4, (Raise For Success) then largest residual in 1^st iteration will reduce to ________.

• Zero Correct
• 4
• -1
• -1

Question No 3:

Relaxation (Raise For Success) Method is a/an _______.

• Direct Method
• Iterative Method Correct

Question No 4:

The 3^rd row of the augmented matrix of the system of linear equation (Raise For Success) is 2x+z=4 , X-y+z=3 , -y+z=-5

• 1 , -1 and -5
• 0 , -1 , 1 and -5 Correct
• 1 . -1 . 0 and 5
• 0 , -1 , 3 and -5

Question No 5:

If there are three equations in (Raise For Success) the two variables, then which of the following is true?

• System may have unique solutions
• System may have multiple numbers of finite solutions
• System may have infinite many solutions
• All above possibilities exist depends on the coefficients of variable’s Correct

Question No 6:

In ______ method, a (Raise For Success) system is reduced to an equivalent diagonal from using elementary transformations.

• Jacobi’s
• Gauss-Seidel
• Relaxation
• Gaussian elimination Correct

Question No 7:

The determination (Raise For Success) of a _____ matrix is the product of the diagonal elements.

• Diagonal Correct
• Upper triangular
• Lower triangular
• Scalar

Question No 8:

While using Relaxation method, which of the following is the Residuals for (Raise For Success) 1^st iteration on the system 2x+3y = 1 , 3x+2=4?

• (2,3) Correct
• (3,-2)
• (-2,3)
• (1,4)

Question No 9:

Which one of the (Raise For Success) following is a two-points method?

• Newton-Raphson Method
• Secant Method Correct
• Muller’s Method
• Method of iteration

Question No 10:

An eigenvector V is said to be normalized if the coordinate of (Raise For Success) largest magnitude is equal to ____.

• Unity Correct
• Zero

Question No 11:

While solving a system of linear equations by Gauss Jordon Method (Raise For Success) after all the elementary row operations if there lefts also zeros on the main diagonal then:

• System may have unique solutions Correct
• System has no solution
• System may have multiple numbers of finite solutions
• System may have infinite many solutions

Question No 12:

The power method can be used only to find the eigenvalue of A that (Raise For Success) is largest in absolute value-we call this eigenvalue the dominant:

• True Correct
• False 

Question No 13:

While solving the system: x-2y=1, x+4y=4 by Gauss-Seidel method (Raise For Success) which of the following ordering is feasible to have good approximate solution?

• X+4y=1 , x-2y=4 Correct
• X+2y=1 , x-4y=4
• X+4y=4 , x=2y=1
• No need to reorder

Question No 14:

Gauss elimination and Gauss Jordan methods are popular among many (Raise For Success) methods for finding the ____ of a matrix.

• Identify Correct
• Transpose
• Inverse
• None of the given choices

Question No 15:

Question No 16:

Two matrices with the same characteristic polynomial need not be similar.

• True Correct
• False

Question No 17:

Direct methods can be (Raise For Success) more rapid than iterative algorithms.

• True Correct
• False

Question No 18:

Question No 19:

Gauss-Seidel (Raise For Success) method is similar to ______

• Iterations method Correct
• Regula-Falsi method
• Jacobi’s method
• None of the given choices

Question No 20:

If the product of two matrices is an identify matrices that is AB=I, then (Raise For Success) which of the following is true?

• A is transpose of B
• A is inverse of B Correct
• A is singular
• B is singular

Question No 21:

For differences methods (Raise For Success) we require the set of values.

• True Correct
• False

Question No 22:

Which is the following is a reason due to which the LU decomposition of (Raise For Success) the system of linear equations: x+y=1,x+y=2 is not possible?

• Associated coefficient matrix is singular
• All values of I’s and u’s can’t be evaluated
• Determinant of coefficient matrix is zero
• All are equivalent Correct

Question No 23:

A 3x3 identity matrix (Raise For Success) have three and different Eigen values.

• True
• False Correct

Question No 24:

If A is a non-triangular matrix (upper triangular, lower triangular) or (Raise For Success) diagonal matrix, the eigenvalues of A are the diagonal entries of A.

• True Correct
• False 

Question No 25:

Eigenvalues of a (Raise For Success) symmetric matrix are all _______.

• Real Correct
• Complex
• Zero
• Positive

Question No 26:

Non-convergence in Newton-Raphson method can occur if the initial value (Raise For Success) is selected such that the derivative of the function equals to:

• Infinity
• Zero Correct
• One
• Negative infinity

Question No 27:

In Gauss-Seidel method each equation of the system is solved for the (Raise For Success) unknown with _____ coefficient, in terms of remaining unknowns:

• Smallest
• Largest Correct
• Any positive
• Any negative

Question No 28:

Question No 29:

Question No 30: