**Example 5:** Find the value of in if its determinant has a value of .

This is not a "trick" question. We can actually find the value of "x" such that when we apply the formula we get −12.

Get the determinant of the given matrix and set it equal to −16. By doing so, we generate a simple linear equation that is solvable for "x".

Checking our answer: Replace "x" by 7, then solve for the determinant. We expect to get −12.

This verifies that our solution is correct!