Question

Find the value of $\left|\begin{array}{ccc}53& 106& 159\\ 52& 65& 91\\ 102& 153& 221\end{array}\right|$

Answer 1

$\left[\begin{array}{ccc}53& 106& 159\\ 52& 65& 91\\ 102& 153& 221\end{array}\right]$

$=53\times \left[\begin{array}{cc}65& 91\\ 153& 221\end{array}\right]-106\times \left[\begin{array}{cc}52& 91\\ 102& 221\end{array}\right]+159\times \left[\begin{array}{cc}52& 65\\ 102& 153\end{array}\right]$

$=0$