Thread: Augmented Matrix Consistency

I have this Linear Alg problem:

Determine value(s) of h such that the matrix is an augmented matrix of a consistent linear system:

[ 1 h -3 ]
[ -1 2 3 ]


Now I started by getting it into triangular form, but from there, I had no clue what to do. How do I find the possible values of h to make it consistent?

if a system is inconsistent then it would have a row of zero's equal to a number so you would need to ensure h is a value that does not create this.

Okay, I understand that. However, what exactly is the process of solving such a problem. My teacher's notes say that I need to put the matrix in triangular form.

[ 1 h -3 ]
[ -2 4 6 ]


[ 1 h -3 ]
[ -1 2 3 ] (1/2)R2


[ 1 h -3 ] R1 + R2 = R2
[ 0 h+2 0 ]


If I understand correctly, should I be looking at where h+2 is either equal to 1 or 0?

yes you would need to make sure the bottom line had no numbers equal to zero and so h+2 would need to equal zero (however this system is redundant e.g. it has infinitly many solutions)