MTH603 Quiz 2 Solution and Discussion


If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the following will be the orders of its decomposed matrices; ‘L’ and ‘U’? MTH603
Order of ‘L’ = 31, Order of ‘U’ = 1*3

@cyberian said in MTH603 Quiz 2 Solution and Discussion:
In ………… method, matrix [A] of the system of equations is decomposed into the product of two matrices [L] and [U], where [L] is a lowertriangular matrix and [U] is an uppertriangular matrix with 1’s on its main diagonal.
MTH603
GaussSeidel
Crout’s ReductionMethodCrout’s ReductionMethod
Here the coefficient matrix [A] of the system of equations is decomposed into the product of two matrices
[L] and [U], where [L] is a lowertriangular matrix and [U] is an uppertriangular matrix with 1’s on its
main diagonal.

In ………… method, matrix [A] of the system of equations is decomposed into the product of two matrices [L] and [U], where [L] is a lowertriangular matrix and [U] is an uppertriangular matrix with 1’s on its main diagonal.
MTH603
GaussSeidel
Crout’s ReductionMethod

@cyberian said in MTH603 Quiz 2 Solution and Discussion:
If the determinant of a matrix A is not equal to zero then the system of equations will have……….
A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is nonzero. If this determinant is zero, then the system has an infinite number of solutions.

If the determinant of a matrix A is not equal to zero then the system of equations will have……….

While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x 3y = 1, 3x 2y =4 ?
MTH603
(2,3)

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 ?

In GaussSeidel method, each equation of the system is solved for the unknown with  coefficient, in terms of remaining unknowns.

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

Under iterative methods, the initial approximate solution is assumed to be…………. MTH603
Known
![0_1592208904558_cebc879771904a5ab290abe496d4a5adimage.png](Uploading 100%)

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%)

While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system;
2x+3y = 1, 3x +2y =  4 ?

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.

@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.

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