Question

In Problems $32$and$33$, use properties of determinants to find the value of each determinant if it is known that$\left|\begin{array}{cc}x& y\\ a& b\end{array}\right|=8$

$\left|\begin{array}{cc}2x& y\\ 2a& b\end{array}\right|$

Short answer

If$\left|\begin{array}{cc}x& y\\ a& b\end{array}\right|=8$, then the value of the determinant$\left|\begin{array}{cc}2x& y\\ 2a& b\end{array}\right|$ is$16$

Step-by-step solution

Step 1. Given data

The given determinant is

$\left|\begin{array}{cc}x& y\\ a& b\end{array}\right|=8$

The value of determinant need to find out is

role="math" localid="1646934897550" $\left|\begin{array}{cc}2x& y\\ 2a& b\end{array}\right|$

Step 2. Value of determinant 

According to properties of determinants, if$\left|\begin{array}{cc}l& m\\ n& o\end{array}\right|=p$

then$\left|\begin{array}{cc}kl& m\\ kn& o\end{array}\right|=kp$

So

$$\begin{gathered} \left|\begin{array}{cc}2x& y\\ 2a& b\end{array}\right|=2\left(8\right) \\ \left|\begin{array}{cc}2x& y\\ 2a& b\end{array}\right|=16 \end{gathered}$$