Question

Find the value of each determinant.

23.$\left|\begin{array}{cc}15& 11\\ 23& 19\end{array}\right|$

Short answer

The value of the determinant $\left|\begin{array}{cc}15& 11\\ 23& 19\end{array}\right|=32$.

Step-by-step solution

- Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$.

- Find the determinant

Apply the definition of the method of finding determinant of second order

matrix $\left|\begin{array}{cc}15& 11\\ 23& 19\end{array}\right|$.

$\left|\begin{array}{cc}15& 11\\ 23& 19\end{array}\right|=15\times \left(19\right)-\left(23\right)\left(11\right)$

- Simplify

To further simplify multiply the values first.

$\begin{array}{c}\left|\begin{array}{cc}15& 11\\ 23& 19\end{array}\right|=15\times \left(19\right)-\left(23\right)\left(11\right)\\ =\text{285}-\text{253}\\ =32\end{array}$