Chiò’s Method

Use Chiò’s Method to find each determinant.

• (a)  $\begin{vmatrix}1&2&3\\ 4&5&6\\ 7&8&9\end{vmatrix}$     (b)  $\begin{vmatrix}2&1&4&0\\ 0&1&4&0\\ 1&1&1&1\\ 0&2&1&1\end{vmatrix}$

What if $a_{1,1}$ is zero?

The Rule of Sarrus is a mnemonic that many people learn for the $3\!\times\!3$ determinant formula. To the right of the matrix, copy the first two columns.

Then the determinant is the sum of the three upper-left to lower-right diagonals minus the three lower-left to upper-right diagonals $aei+bfg+cdh-gec-hfa-idb$. Count the operations involved in Sarrus’s formula and in Chiò’s.

Prove Chiò’s formula.