Question

determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
row 1: 1 -1 4
row 2: -2 3 h

Answer 1

ok
step 1: row 2 -> add to 2*row 1
1 -1 4
0 1 (h+8)

maybe im doing this wrong but it seems like h could be any real number and this would still be a consistent system
??

Answer 2

well thats the answer. and now I know why. Thank you very much.

Just for a bit more detail. When solving something like this, what should I do?

Answer 3

think of it like elimination
use row operations to get all zeroes below the diagonal of the matrix
if you end up with all 1's in the diagonal, there is 1 solution, consistent system
if a row ends up with all zeroes, dependent system, infinite solutions
if a row ends up with all zeroes except for last column, No solution, inconsistent system