Question

Find the value of each determinant.

26.$\left|\begin{array}{cc}-3.2& -5.8\\ 4.1& 3.9\end{array}\right|$

Short answer

The value of the determinant $\left|\begin{array}{cc}-3.2& -5.8\\ 4.1& 3.9\end{array}\right|=\text{11.3}$.

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 $\left|\begin{array}{cc}-3.2& -5.8\\ 4.1& 3.9\end{array}\right|$.

$\left|\begin{array}{cc}-3.2& -5.8\\ 4.1& 3.9\end{array}\right|=-3.2\times \left(3.9\right)-\left(-5.8\right)\left(4.1\right)$

- Simplify

To further simplify multiply the values first.

$\begin{array}{c}\left|\begin{array}{cc}-3.2& -5.8\\ 4.1& 3.9\end{array}\right|=-3.2\times \left(3.9\right)-\left(-5.8\right)\left(4.1\right)\\ =-\text{12.48}+\text{23.78}\\ =\text{11.3}\end{array}$