Q.32 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

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 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

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

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 

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