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 linear equations representing the given information have

Unique solution

$X=A^{-1}B=\begin{bmatrix}x\\y\\z\end{bmatrix}=\frac{-1}{3}\begin{bmatrix}-1 & -1 & 6\\-1 & 2 & -6\\2 & -1 & -3\end{bmatrix}\begin{bmatrix}37000\\47000\\12000\end{bmatrix}$

$\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}4000\\5000\\3000\end{bmatrix}$