Question

Find the value of each determinant.

$\left|\begin{array}{cc}7& 5.2\\ -4& 1.6\end{array}\right|$

Short answer

The value of the determinant $\left|\begin{array}{cc}7& 5.2\\ -4& 1.6\end{array}\right|=32$.

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 $\left|\begin{array}{cc}7& 5.2\\ -4& 1.6\end{array}\right|$.

$\left|\begin{array}{cc}7& 5.2\\ -4& 1.6\end{array}\right|=7\times \left(1.6\right)-\left(-4\right)\left(5.2\right)$

- Simplify

To further simplify multiply the values first.

$\begin{array}{c}\left|\begin{array}{cc}7& 5.2\\ -4& 1.6\end{array}\right|=7\times \left(1.6\right)-\left(-4\right)\left(5.2\right)\\ =\text{11.2}+\text{20.8}\\ =\text{32}\end{array}$