# Determinant of $\left[\begin{array}{cc}- 12 e^{- 4 r} \sin{\left(3 \theta \right)} & 9 e^{- 4 r} \cos{\left(3 \theta \right)}\\4 e^{4 r} \cos{\left(3 \theta \right)} & - 3 e^{4 r} \sin{\left(3 \theta \right)}\end{array}\right]$

The calculator will find the determinant of the square $2$x$2$ matrix $\left[\begin{array}{cc}- 12 e^{- 4 r} \sin{\left(3 \theta \right)} & 9 e^{- 4 r} \cos{\left(3 \theta \right)}\\4 e^{4 r} \cos{\left(3 \theta \right)} & - 3 e^{4 r} \sin{\left(3 \theta \right)}\end{array}\right]$, with steps shown.

Related calculator: Cofactor Matrix Calculator

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Calculate $\left|\begin{array}{cc}- 12 e^{- 4 r} \sin{\left(3 \theta \right)} & 9 e^{- 4 r} \cos{\left(3 \theta \right)}\\4 e^{4 r} \cos{\left(3 \theta \right)} & - 3 e^{4 r} \sin{\left(3 \theta \right)}\end{array}\right|$.
The determinant of a 2x2 matrix is $\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$.
$\left|\begin{array}{cc}- 12 e^{- 4 r} \sin{\left(3 \theta \right)} & 9 e^{- 4 r} \cos{\left(3 \theta \right)}\\4 e^{4 r} \cos{\left(3 \theta \right)} & - 3 e^{4 r} \sin{\left(3 \theta \right)}\end{array}\right| = \left(- 12 e^{- 4 r} \sin{\left(3 \theta \right)}\right)\cdot \left(- 3 e^{4 r} \sin{\left(3 \theta \right)}\right) - \left(9 e^{- 4 r} \cos{\left(3 \theta \right)}\right)\cdot \left(4 e^{4 r} \cos{\left(3 \theta \right)}\right) = - 36 \cos{\left(6 \theta \right)}$
$\left|\begin{array}{cc}- 12 e^{- 4 r} \sin{\left(3 \theta \right)} & 9 e^{- 4 r} \cos{\left(3 \theta \right)}\\4 e^{4 r} \cos{\left(3 \theta \right)} & - 3 e^{4 r} \sin{\left(3 \theta \right)}\end{array}\right| = - 36 \cos{\left(6 \theta \right)}$A