MTH603 Quiz 2 Solution and Discussion

@zaasmi said in MTH603 Quiz 2 Solution and Discussion:
While solving a system of linear equations by Gauss Jordon Method, after all the elementary row operations if there lefts also zeros on the main diagonal then which of the is true about the system?
System may have unique solutions
System has no solution
System may have multiple numbers of finite solutions
System may have infinite many solutions 
@zaasmi said in MTH603 Quiz 2 Solution and Discussion:
While solving a system of linear equations, which of the following approach is economical for the computer memory?
Direct
Iterative (Page 69)
Analytical
Graphical 
In Jacobi’s Method, We assume that the …………elements does not vanish.
Diagonal
Offdiagonal
Row
Column

Which of the following is a reason due to which the LU decomposition of the system of linear equations; x+y = 1, x+y =2 is not possible?



Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form

@zaasmi said in MTH603 Quiz 2 Solution and Discussion:
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form
(a) The given linear equation is
2x + 0y + 9 = 0
⇒ 2x + 9 = 0
⇒ 2x = 9
⇒ x=  9/2 and y can be any real number.
Hence, (9/2 , m) is the required form of solution of the given linear equation. 
Which of the following rearrangement make strictly diagonal dominant, the system of linear equations; x3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
–6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
No need to rearrange as system is already in diagonal dominant form.

While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system;
2x+3y = 1, 3x +2y =  4 ? 
When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the method is
……………. MTH603Stable
![0_1592208804427_990b174155b2422c923d19f41007b0a3image.png](Uploading 100%) 
Under iterative methods, the initial approximate solution is assumed to be…………. MTH603
Known
![0_1592208904558_cebc879771904a5ab290abe496d4a5adimage.png](Uploading 100%) 
If a system of equations has a property that each of the equation possesses one large coefficient and the larger coefficients in the equations correspond to different unknowns in different equations, then which of the following iterative method id preferred to apply?
MTH603
GaussSeidel method 
In GaussSeidel method, each equation of the system is solved for the unknown with  coefficient, in terms of remaining unknowns.