If \(\left| \begin{array}{cc} -x & 2 \\ 4x &1 \end{array} \right|\) = \(\left| \begin{array}{cc} 3 & 3x \\ 4 & -5 \end{array} \right|\), find the value of x
A
5
B
2
C
-2
D
-5
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\left| \begin{array}{cc} -x & 2 \\ 4x &1 \end{array} \right|\) = \(\left| \begin{array}{cc} 3 & 3x \\ 4 & -5 \end{array} \right|\),
Means that the determinants of both Matrices are equal
- x - 8x = -15 - 12x
-9x = -15 - 12x
12x - 9x = - 15
3x = -15
x = \(\frac{-15}{3}\) = -5
Source: Myschool Past Questions Archive (Record #76304)