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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 2x-0y-2=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 = 2

Anything times zero is zero.
0x + 0y = 2

Anything times zero is zero.
0 + 0y = 2

Combine like terms: 0 + 0 = 0
0 = 2

Solving
0 = 2

Couldn’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 non-diagonal elements in that row for each row of the matrix.

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