Answer:
In order to have a consistent linear system represented by the augmented matrix:
the value of h must be:
Step-by-step explanation:
A system is consistent if it has a solution, this solution can be unique or a set of infinite solutions.
First, you take the augmented matrix and find the equivalent row echelon form using Gaussian-Jordan elimination:
To do this, you have to multiply the 1st row by 3 and add it to the 2nd row, the resulting matrix is:
Now, write the system of equations:
The only way this system has a solution is if 5+3h=0, then, to satisfy this, the value of h must be: