# Algebraic Equations Questions and Answers – Solution of Linear Simultaneous equation using Iterative Methods

This set of Numerical Methods MCQs focuses on “Solution of Linear Simultaneous Equation using Iterative Methods”.

1. The time taken to solve a system of equations using direct method is more than the time taken by iterative methods.
a) True
b)False

Explanation: The time taken to solve a system of equations using direct method is less than the time taken by iterative methods because direct methods involve less computations than iterative methods.

2. The process of constructing a sequence of vectors and obtaining the solution of a system using specified accuracy is called _________
a) Elimination
b) Reduction
c) Iteration
d) Raphson method

Explanation: The process of constructing a sequence of vectors and obtaining the solution of a system using specified accuracy is called iteration. Elimination and reduction are not sequential processes. Raphson method is a method which is employed for finding the roots of an equation through some different procedure.

3. Numerical techniques more commonly involve _______
a) Iterative method
b) Direct method
c) Elimination method
d) Reduction method

Explanation: Numerical techniques more commonly involve an iteration method due to the degree of accuracy involved. This is because, iterations reduce the approximation errors which may occur in numerical problems. They perform sequential operations which in turn increases the accuracy.

4. What is the primary drawback of using direct methods of solution?
a) They yield solution after a certain amount of fixed computation
b) They have large calculations involved
c) They make use of back substitution
d) They do not achieve the desirable accuracy

Explanation: The drawback of using direct methods of solution is that these methods yield solution after a certain amount of fixed computation. There are no calculations and back substitution in direct methods. Their accuracy is less than that of iterative methods, but that is not the primary drawback.

5. In an iterative method, the amount of computation depends on the _________
a) Number of variables
b) Degree of accuracy
c) Rounding of errors
d) Ease of using the operators

Explanation: In an iterative method, the amount of computation depends on the degree of accuracy required. More is the accuracy required, more will be the number of computations involved.

6. Iteration is also called as ________
a) Accurate process
b) Self-correcting process
c) Approximate process
d) Rounding off process

Explanation: Iteration is also called as self-correcting process as with the sequence of operations, accuracy increases accompanied by corrections in the process. Any error made at any stage of computation gets automatically corrected in the subsequent steps.

7. Which of the following is an iterative method?
a) Gauss Jordan
b) Gauss Elimination
c) Gauss seidal
d) Factorization

Explanation: Gauss seidal method is an iterative method. Gauss elimination is based upon elimination of unknowns. Gauss Jordan is based on back substitution as well as elimination. Factorization is based upon formation of two triangular matrices with a matrix.

8. Why iterative methods are called as self correcting?
a) Iterations involve repetition
b) Checks occurring during the process ensure that the errors are reduced
c) Any error made at any stage of computation gets automatically corrected in the subsequent steps
d) After each step, validity of the method is checked.

Explanation: Any error made at any stage of computation gets automatically corrected in the subsequent steps that’s why iterative methods are called self-correcting.

9. Which of the following is not an iterative method?
a) Jacobi’s method
b) Gauss Seidal method
c) Relaxation method
d) Gauss Jordan 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.

10. Number of iteration depends on the _________
a) Initial value taken to start the iteration
b) Type of linear equations
c) Number of unknowns
d) Approximations to be done

Explanation: Number of iteration depends on the initial value taken to start the iteration. The initial value shows the amount of accuracy that has to be achieved. And we know that, more is the accuracy required, more will be the number iterations.

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