Question

Find the value of each determinant.

44.

$\left|\begin{array}{cc}\mathbf{-}\mathbf{5}& \mathbf{2}\\ \mathbf{4}& \mathbf{9}\\ & \end{array}\right|$

Short answer

The value of the given determinant is $\mathbf{-}\mathbf{53}$.

Step-by-step solution

­- Description of step.

The value of a second-order determinant can be found out by calculating difference of product of two diagonals.

$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$

­- Find the value of the determinant.

The value of the determinant $\left|\begin{array}{cc}-5& 2\\ 4& 9\end{array}\right|$is given by:

$\begin{array}{c}\left|\begin{array}{cc}-5& 2\\ 4& 9\end{array}\right|=\left(-5\right)\left(9\right)-\left(4\right)\left(2\right)\\ =-45-8\\ =-53\end{array}$

­- Description of step.

The value of the given determinant is $-53$.