Question

can anyone tell me the condition for consistent matrix???

Answer 1

Equations

All the systems of equations that we have seen in this section so far have had unique solutions. These are referred to as Consistent Systems of Equations, meaning that for a given system, there exists one solution set for the different variables in the system or infinitely many sets of solution. In other words, as long as we can find a solution for the system of equations, we refer to that system as being consistent

For a two variable system of equations to be consistent the lines formed by the equations have to meet at some point or they have to be parallel.

For a three variable system of equations to be consistent, the equations formed by the equations must meet two conditions:

All three planes have to parallel

Any two of the planes have to be parallel and the third must meet one of the planes at some point and the other at another point.

Given that such systems exist, it is safe to conclude that Inconsistent systems should exist as well, and they do. Inconsistent Systems of Equations are referred to as such because for a given set of variables, there in no set of solutions for the system of equations.

Inconsistent systems arise when the lines or planes formed from the systems of equations don't meet at any point and are not parallel (all of them or only two and the third meets one of the planes at some point.)