Determine the value (or values) of h such that the matrix: 2 - 3 h - 6 9 5 is the augmented matrix of a consistent linear system.

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:

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