MTH603 Grand Quiz Solution and Discussion

 How many assumptions are there in Jacobi’s method?
a) 2
b) 3
c) 4
d) 5
 How many assumptions are there in Jacobi’s method?

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
 Which of the following is an assumption of Jacobi’s method?
a) The coefficient matrix has no zeros on its main diagonal
b) The rate of convergence is quite slow compared with other methods
c) Iteration involved in Jacobi’s method converges
d) The coefficient matrix has zeroes on its main diagonal
Answer: a
Explanation: This is because it is the method employed for solving a matrix such that for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (nondiagonal) entries in that row. This helps in converging the result and hence it is an assumption.  Which of the following is an assumption of Jacobi’s method?

 Which of the following is an assumption of Jacobi’s method?
a) The coefficient matrix has no zeros on its main diagonal
b) The rate of convergence is quite slow compared with other methods
c) Iteration involved in Jacobi’s method converges
d) The coefficient matrix has zeroes on its main diagonal
 Which of the following is an assumption of Jacobi’s method?

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
 The Jacobi iteration converges, if A is strictly dominant.
a) True
b) False
Answer: a
Explanation: If A is matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (nondiagonal) entries in that row, and for such matrices only Jacobi’s method converges to the accurate answer.  The Jacobi iteration converges, if A is strictly dominant.

 The Jacobi iteration converges, if A is strictly dominant.
a) True
b) False
 The Jacobi iteration converges, if A is strictly dominant.

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
 The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along ________
a) Leading diagonal
b) Last column
c) Last row
d) Nonleading diagonal
View Answer
Answer: a
Explanation: The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along the leading diagonal because convergence can be achieved only through this way.  The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along ________

 The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along ________
a) Leading diagonal
b) Last column
c) Last row
d) Nonleading diagonal
View Answer
 The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along ________

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
In J
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@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
https://cyberian.pk/topic/838/mth603midtermpastandcurrentsolvedpaperdiscussion
SLOW

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
https://cyberian.pk/topic/838/mth603midtermpastandcurrentsolvedpaperdiscussion

In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
For the system of equations; x =2, y=3. The inverse of the matrix associated with its coefficients is.
⌈ 3 2⌉ ⌈ x ⌉ = ⌈ 5 ⌉
⌊ 4 3⌋ ⌊ y ⌋ ⌊ 2 ⌋⌈ x ⌉ = (1/17) ⌈ 3 2 ⌉ ⌈ 5 ⌉
⌊ y ⌋ ⌊ 4 3 ⌋ ⌊2⌋⌋= (1/17)⌈11⌉ ⌊26⌋ = ⌈11/17⌉ ⌊26/17⌋
x = 11/17 and y = 26/17

For the system of equations; x =2, y=3. The inverse of the matrix associated with its coefficients is.

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
The linear equation: x+y=1 has  solution/solutions.
This is an stand alone linear equation in two variables. It would have infinite number or solutions. Assign any real value to x, there would be a corresponding real value of y. All these pairs of values are solution of the equation.

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

@zaasmi said in MTH603 Grand Quiz Solution and Discussion:
Gauss–Seidel method is also known as method of …………….
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 system of linear equations.

Gauss–Seidel method is also known as method of …………….