MTH603 Quiz 1 Solution and Discussion

@cyberian said in MTH603 Quiz 1 Solution and Discussion:
the linear equation 2x0y2=0 has

@cyberian said in MTH603 Quiz 1 Solution and Discussion:
A system is inconsistent if it has no solution. In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution.
Two Variables
In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution. 
@cyberian said in MTH603 Quiz 1 Solution and Discussion:
The primary use of iterative methods is for computing the solution to large, sparse systems and for finding a few eigenvalues of a large sparse matrix. Along with other problems, such systems occur in the numerical solution of partial differential equations.
This chapter discusses the use of iterative methods in the solution of partial differential equations. Most of the large sparse systems, which are solved by iterative methods, arise from discretizations of partial differential equations. The value of a particular generality is a function of the problem or class of problems to be solved. Three basic parts of a computer program to solve a boundaryvalue problem are the mesh generation, the discretization, and the solution of the matrix problem. The mesh generation and the discretization parts determine the accuracy or value of the numerical solution, while the matrix solution part determines most of the computer solution cost. These three parts are not independent of each other. Increased generality in the mesh generation and discretization parts can significantly increase the matrix solution cost. Thus, solution cost can only be given as a function of the mesh decomposition and discretization methods under consideration. The factors that mostly affect matrix solution costs are total arithmetic operations required, storage requirements, and overhead because of data transmission and logical operations associated with the implementation of the solution method. The most efficient solution procedures usually are those that minimize storage and arithmetic requirements.

A system is inconsistent if it has no solution. In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution.

The primary use of iterative methods is for computing the solution to large, sparse systems and for finding a few eigenvalues of a large sparse matrix. Along with other problems, such systems occur in the numerical solution of partial differential equations.

the linear equation 2x0y2=0 has

Solution to the linear equation 2x + 0y = 0

while using relaxation method, which of th folowing is the

In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in.

Simplifying
0x + 0y = 2Anything times zero is zero.
0x + 0y = 2Anything times zero is zero.
0 + 0y = 2Combine like terms: 0 + 0 = 0
0 = 2Solving
0 = 2Couldn’t find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.

A square matrix is said to be diagonally dominant if the magnitude of the diagonal element in a row is greater than or equal to the sum of the magnitudes of all the other nondiagonal elements in that row for each row of the matrix.

The root of the equation 3x−ex=0 is bounded in the interval.

@zaasmi said in MTH603 Quiz 1 Solution and Discussion:
The first row of the augmented matrix of the system of linear equations is: 2x+z=4 xy+z=3 y+z=5

The first row of the augmented matrix of the system of linear equations is: 2x+z=4 xy+z=3 y+z=5


@zaasmi said in MTH603 Quiz 1 Solution and Discussion:
If there are three equations in two variables, then which of the following is true?
Dependent Systems of Equations with Three Variables
We know from working with systems of equations in two variables that a dependent system of equations has an infinite number of solutions. The same is true for dependent systems of equations in three variables. An infinite number of solutions can result from several situations. The three planes could be the same, so that a solution to one equation will be the solution to the other two equations. All three equations could be different but they intersect on a line, which has infinite solutions (see below for a graphical representation). Or two of the equations could be the same and intersect the third on a line (see the example problem for a graphical representation).
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