# Linear algebra: augmented matrix of a consistent system

1. Aug 27, 2011

### abjf9299

1. The problem statement, all variables and given/known data

Determine the values of h such that the matrix is the augmented matrix of a consistent linear system.
[1 h -5]
[2 -8 6]

2. Relevant equations

None that I know of.

3. The attempt at a solution

Multiplied row (1) by -2:
[-2 -2h 10 ]
[ 2 -8 6 ]

and added together to get: -2h -8 = 16
and of course you can solve that for -2h=24
and h = -12.

So is it correct to say H can be any value other than -12 in order to make the system consistent? Please let me know if its correct. If not, please tell me what I need to do to get the correct answer. Thanks!

2. Aug 27, 2011

### rock.freak667

[-2 -2h 10 ]
[ 2 -8 6 ]

If you add together row 1 and 2 you will get

[-2 -2h 10]
[0 (-2h-8) 16]

so yes -2h-8= 16 is one equation but will your matrix still be consistent if -2h-8 = 0?

3. Aug 27, 2011

### vela

Staff Emeritus
Also, remember the matrix consists of only the coefficients of the equations. That second line corresponds to the equation (-2h-8)y = 16.

What does it mean when a system is said to be consistent? How can that idea be related to that second equation?