MTH603 Grand Quiz Solution and Discussion

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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.

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Jacobi’s Method is a/an………………

Iterative method
Direct method

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Whileusingtherelaxationmethodforfindingthesolutionofthefollowingsystem8x1+3x2−2x3=5 4x1+7x2+2x3=9 3x1+5x2+9x3=2withtheinitialvector(0,0,0),theresidualswouldbe

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Gauss - Jordan Method is similar to ……….

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

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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

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Choleskey’s reduction method is also called
Bisection method

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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

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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

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The linear equation: x+y=1 has --------- solution/solutions.

no solution
unique
infinite many
finite many

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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

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@zaasmi said in MTH603 Grand Quiz Solution and Discussion:

Gauss–Seidel method is similar to ……….

In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.

[zaasmi]

Gauss–Seidel method is similar to ……….

Iteration’s method
Regula-Falsi method
Jacobi’s method
None of the given choices

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3x4−2x2−24=0 has at least−−−−complex root(s)?

1
2
3
4

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While using Jacobi method for the matrix

A=⎡⎣⎢⎢200021012⎤⎦⎥⎥
the value of ‘theta θ’ can be found as

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If A=⎡⎣⎢⎢⎢⎢⎢231024039⎤⎦⎥⎥⎥⎥⎥then by using Gaussian Elimination method the value of A−1 will be

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While using the Gauss-Seidel Method for finding the solution of the following system
3x+y+z=11
2x+5y−z=16
x+y+5z=4

with initial guess (0,0,0), the next iteration would be