1. ## Matrix urgent

Hey I've reduced the matrix to what it's asked me to which is

1 - 1 - 1 - 9
0 - 1 - -1 - 5
0 - 0 - 0 - K+5

It's the second part of the question I don't understand, describe the behaviour when k doesn't equal -5 and when it does it equal -5 by stating that the equations are inconsistent or finding the reduced echelon matrix? Anyone shed any light on this? Thanks

2. Originally Posted by Mathsnewbie
Hey I've reduced the matrix to what it's asked me to which is

1 - 1 - 1 - 9
0 - 1 - -1 - 5
0 - 0 - 0 - K+5

It's the second part of the question I don't understand, describe the behaviour when k doesn't equal -5 and when it does it equal -5 by stating that the equations are inconsistent or finding the reduced echelon matrix? Anyone shed any light on this? Thanks
You have not mantioned whether the system you are dealing with is homogeneous or non homogeneous.
In case of NON-HOMOGENEOUS SYSTEM:
The system has no solution if the rank of the matrix is not equal to the rank of the augmented matrix.
here if K is not equal to -5 than the rank of the matrix of the augmented matrix becomes 3 whereas the rank of the matrix of coefficients is 2,so the systems becomes inconsistent.That is why the value of k must be -5 for the solution to exist incase of a non-homogeneous system.