# MTH603 Grand Quiz Solution and Discussion

• Under iterative methods, the initial approximate solution is assumed to be………….
Known
UnKnown
Found
No of the given • In Gauss-Jacobi’s method, the corresponding elements of
x(r+1)i
replaces those of
x®i
as soon as they become available.

True
False

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

can be rewritten as

Reff

• If one root of the equation is-3-7i, then the other root will be

-3-7i
-3+7i
3-7i
3+7i  • If one root of the equation is-3-7i, then the other root will be

-3-7i
-3+7i
3-7i
3+7i

• In Jacobi’s Method, We assume that the …………elements does not vanish.

Mathematical Methods for Numerical Analysis and Optimization … Solution of Linear System of Equationsand Matrix Inversion Jacobi’s Method This is an iterative … We also assume that the diagonal element do not vanish.

• In Jacobi’s Method, We assume that the …………elements does not vanish.

Diagonal
Off-diagonal
Row
Column • While using Jacobi method for the matrix A=⎡⎣⎢⎢2−10−120002⎤⎦⎥⎥
and ‘theta θ =pi/4’, the orthogonal matrix S1 • Gauss elimination and Gauss-Jordan methods are popular among many methods for finding the ………of a matrix.

Identity
Transpose
Inverse
None of the given choices • While using power method, the computed vector u(2)=⎛⎝⎜⎜6.5714289.5714211.21423⎞⎠⎟⎟
will be in normalized form as

While using power method, the computed vector [{u^{(2)}} = \left( {\begin{array}{*{20}{c}} {6.571428}\{9.57142}\{11.21423} \end{array}} \right)] will be in normalized form as • In Gauss-Seidel method, each equation of the system is solved for the unknown with -------- coefficient, in terms of remaining unknowns.

110 Solving each equation of the given system for the unknown with the largest coefficient in terms of the remaining unknowns, we have x = 37. Example 19. Solve the following system by Gauss–Seidel method : by Gauss–Seidel • In Gauss-Seidel method, each equation of the system is solved for the unknown with -------- coefficient, in terms of remaining unknowns.

smallest
largest
any positive
any negative

• 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

⎡⎣⎢⎢1000cosθsinθ0−cosθ−sinθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥ Reff

• 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

⎡⎣⎢⎢1000cosθsinθ0−cosθ−sinθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥
⎡⎣⎢⎢cosθ0sinθ010−sinθ0cosθ⎤⎦⎥⎥ • 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 ?

-4
3 REF
2
1   43

4

2

33

1

2

3
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