# MTH603 Grand Quiz Solution and Discussion

• 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 • Two matrices with the _______ characteristic polynomial need not be similar.

same
different

Two similar matrices have the same characteristic polynomial. The converse however is not true in general: two matrices with the same characteristic polynomial need not be similar.

• Jacobi’s Method is a/an………………

Iterative method
Direct method

• Whileusingtherelaxationmethodforfindingthesolutionofthefollowingsystem8x1+3x2−2x3=5 4x1+7x2+2x3=9 3x1+5x2+9x3=2withtheinitialvector(0,0,0),theresidualswouldbe  • Gauss - Jordan Method is similar to ……….

Gauss–Seidel method
Iteration’s method
Relaxation Method
Gaussian elimination method

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

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

• Choleskey’s reduction method is also called
Bisection method

• While using the Gauss-Seidel Method for finding the solution of the system of equation, the following system
2x+2y+z=3
x+3y+z=2
x+y+z=2
can be rewritten as • While using the relaxation method for finding the solution of the below given system, which of the following increment will be introduced? 6x1−2x2+3x3=1
−2x1+7x2+2x3=5
x1+x2−5x3=−13 • The linear equation: x+y=1 has --------- solution/solutions.

no solution
unique
infinite many
finite many

• The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

(x-1)^3
(x+1)^3
x^3-1
x^3+1  | |