MTH603 Grand Quiz Solution and Discussion

• 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

• 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 off-diagonal 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?

• The 2nd row of the augmented matrix of the system of linear equations is:
2x+z=4
x-y+z=-3
-y+z=-5

• If a system of equations has a property that each of the equation possesses one large coefficient and the larger coefficients in the equations correspond to different unknowns in different equations, then which of the following iterative method id preferred to apply?

• While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the system; x-2y =1, x+4y=4 ?

a) (1, 0.75)
b) (0.25,1)
c) (0,0)
d) (1,0.65)

• The dominant eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, smallest absolute value) of that matrix.

Eigenvectors of a matrix corresponding to distinct eigenvalues are linearly independent. ▫. If λ is an eigenvalue of multiplicity k of an n × n matrix A, then the number of … power method converges to the smallest eigenvalue in absolute value of A. … v2, …, vn, and that λ1 is a simple eigenvalue with the largest magnitude, i.e.,.

• While using the Gauss-Seidel Method for finding the solution of the system of equation, the following system
2x+y−3z=5
x+3y+2z=7
x+2y+z=3

can be rewritten as

6

1

2

9

3

1

33

3
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