Two institutions decided to award their employees for resourcefulness, competence and determination in the form of prizes at the rate of Rs. x, Rs. y, Rs. z respectively per person. The first institution decided to award respectively 4, 3 and 2 employees with total prize money Rs. 37,000 and second institution decided to award respectively 5, 3 and 4 employees with the total prize money of Rs. 47,000 for resourcefulness, competence and determination. All the prizes per person together amount to Rs. 12,000.
The value of determinant \(\begin{vmatrix}4 & 3 & 2\\ 5 & 3 & 4\\ 1 & 1 & 1\end{vmatrix}\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −3
Expanding along the first row:
\( \displaystyle \begin{vmatrix}4 & 3 & 2\\ 5 & 3 & 4\\ 1 & 1 & 1\end{vmatrix} = 4\begin{vmatrix}3 & 4\\ 1 & 1\end{vmatrix} - 3\begin{vmatrix}5 & 4\\ 1 & 1\end{vmatrix} + 2\begin{vmatrix}5 & 3\\ 1 & 1\end{vmatrix} \)
\( = 4(3 - 4) - 3(5 - 4) + 2(5 - 3) \)
\( = -4 - 3 + 4 = -3 \)