Two institutions decided to award their employees for resourcefulness competence and determination in the form of prizes at the rate of ₹x, ₹y, ₹z respectively per person. The first institution decided to award respectively 4, 3 and 2 employees with total prize money ₹37.000 and second institution decided to award respectively 5, 3 and 4 employees with the total prize money of ₹47.000 for resourcefulness, competence and determination. All the prizes per person together amount ₹12.000.

The value of determinant $\begin{vmatrix}4 & 3 & 2\\5 & 3 & 4\\1 & 1 & 1\end{vmatrix}$ is:

-3

4(3 - 4) - 3(5 - 4) + 2(5 - 3)

= 4(-1) -3(1) + 2(1) = - 4 - 3 + 4 = -3