Final answer:
To find the value of a, substitute the values from the given matrix into the determinant formula and solve for a. However, the equation is contradictory, indicating that there is no value of a that will make the determinant equal to -19.
Step-by-step explanation:
To find the value of a, we need to find the determinant of the given matrix and set it equal to -19.
Using the formula for the determinant of a 3x3 matrix:
determinant = a(ei - fh) - b(di - fg) + c(dh - eg)
Substituting the values from the matrix:
-19 = (-6(-3)(-3) - 7(4)(-6) + 1(4)(4)) - (1(-3)(-3) - (-6)(4)(-6) + (-6)(4)(4))
Simplifying the equation:
-19 = 27 + 168 + 16 - 9 + 144 - 96
-19 = 270
Since the equation is contradictory, there is no value of a that will make the determinant of the matrix equal to -19.