When solving a system using augmented matricies, how do u know when if the solution is inconsistent, if you continuously are trying to get th identity matrix

The system will be inconsistent if they are not linearly independent. Also you have to remember that identity matrix is always a square matrix.

if your using row reduction to solve the eqution you'll get very obvious fallacies such as 5=0

 

for instance if you have two equation such as

 

x+y=0

 

and

 

x+y=1

 

placed in an augmented matrix, row reduction will yield

 

x+y=0

0=1

 

now you know that 0 cannot equal 1 so something must be wrong, and if you check the original system of equations you'll notice that the two lines are parellel.

 

 

^EVON a system can be consistent if the equations are not linearly independant, this just means that you won't have a unique solution and your solutions will be lines and or planes, or even volumes.

 

for instance if you have two planes intersecting they form a line, this intersection can be represented by a system of simultaneous linear equations composed of the equations for the two planes. this system is consistent and solving it will reveal the equation for the line along which the planes intersect.

 

for a system to be inconsistent there must be no intersection between the equations, with the simplest case being two parrellel lines.