Question

In Problems $7-14$, find the value of each determinant.

$\left|\begin{array}{cc}-4& 0\\ 5& 3\end{array}\right|$

Short answer

The value of the determinant $\left|\begin{array}{cc}-4& 0\\ 5& 3\end{array}\right|$is,$-12$.

Step-by-step solution

Step 1 Given determinant is,

$\left|\begin{array}{cc}-4& 0\\ 5& 3\end{array}\right|$.

Evaluate the determinant.

$\left|\begin{array}{cc}-4& 0\\ 5& 3\end{array}\right|=\left(-4\right)\left(3\right)-5\left(0\right)$

Step 2 Now simplify it.

$$\begin{gathered} \left|\begin{array}{cc}-4& 0\\ 5& 3\end{array}\right|=-12-0 \\ =-12 \end{gathered}$$

Thus, the value of the determinant$\left|\begin{array}{cc}-4& 0\\ 5& 3\end{array}\right|$is,$-12$.