Chapter I, Problem 1PS

To determine

Find the value of the given determinant.

Answer to Problem 1PS

Thevalue of the given determinant is $2$ .

Explanation of Solution

Given:

The given determinant is

  $\left|\begin{array}{cc}-5& -3\\ 4& 2\end{array}\right|$

Calculation:

If $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ is a $2\times 2$ matrix.

Then,

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

Now,

  $\begin{array}{l}\left|\begin{array}{cc}-5& -3\\ 4& 2\end{array}\right|\\ =-5\cdot 2-\left(-3\cdot 4\right)\\ =-10+12\\ =2\end{array}$

Hence the value of the given determinant is $2$ .