MTH603 Quiz 2 Solution and Discussion

• In solving the differential equation
y/=x+y;y(0)=1
h=0.2

By Euler’s method y(0.2) is calculated as

• At which of the following points the Minimum value of 2nd derivative of function
f(x) = -(2/x) in the interval:[1,4] exits?

At x=1

• At which of the following points the Minimum value of 2nd derivative of function
f(x) = -(2/x) in the interval:[1,4] exits?

• 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’ = 3
1, Order of ‘U’ = 1*3

• In ………… method, matrix [A] of the system of equations is decomposed into the product of two matrices [L] and [U], where [L] is a lower-triangular matrix and [U] is an upper-triangular matrix with 1’s on its main diagonal.
MTH603
Gauss-Seidel
Crout’s ReductionMethod

Crout’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 lower-triangular matrix and [U] is an upper-triangular 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 lower-triangular matrix and [U] is an upper-triangular matrix with 1’s on its main diagonal.
MTH603
Gauss-Seidel
Crout’s ReductionMethod

• 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 non-zero. 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 Gauss-Seidel 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
Gauss-Seidel method

• Under iterative methods, the initial approximate solution is assumed to be…………. MTH603
Known

• When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the method is
……………. MTH603

Stable

• 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; x-3y+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.

4

5

43

1

4

2

3

1
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