Question

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

$\left|\begin{array}{cc}3& 4\\ 1& 2\end{array}\right|$

Short answer

The value of the determinant $\left|\begin{array}{cc}3& 4\\ 1& 2\end{array}\right|$is,$2$.

Step-by-step solution

Step 1 Given determinant is,

$\left|\begin{array}{cc}3& 4\\ 1& 2\end{array}\right|$

Now evaluate the given determinant.

$\left|\begin{array}{cc}3& 4\\ 1& 2\end{array}\right|=3\left(2\right)-4\left(1\right)$

Step 2 Now simplify it.

$$\begin{gathered} \left|\begin{array}{cc}3& 4\\ 1& 2\end{array}\right|=6-4 \\ =2 \end{gathered}$$

Thus the value of determinant $\left|\begin{array}{cc}3& 4\\ 1& 2\end{array}\right|$is,$2$.