MTH603 Grand Quiz Solution and Discussion

1. 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

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

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 (non-diagonal) entries in that row, and for such matrices only Jacobi’s method converges to the accurate answer.

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

1. The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along ________
b) Last column
c) Last row

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.

1. The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along ________
b) Last column
c) Last row

• In J

S

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

https://cyberian.pk/topic/838/mth603-mid-term-past-and-current-solved-paper-discussion

SLOW

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

https://cyberian.pk/topic/838/mth603-mid-term-past-and-current-solved-paper-discussion

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

• 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-----------.

• 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.

• 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 …………….

• Differences methods are iterative methods. yes or no

1. Which of the following is not an iterative method? Explanation: Jacobi’s method, Gauss Seidal method and Relaxation method are the iterative methods and Gauss Jordan method is not as it does not involves repetition of a particular set of steps followed by some sequence which is known as iteration.

• Differences methods are iterative methods. yes or no

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1

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