Question

Use either elementary row or column operations, or cofactor expansion, to find the determinant by hand. Then use a software program or a graphing utility to verify your answer. 4 2 3 0 4 0 3 8 3 STEP 1: Expand by cofactors along the second row. 4 0 3 2 4 8 3 0 3 = 4 STEP 2: Find the determinant of the 2x2 matrix found in Step 1. STEP 3: Find the determinant of the original matrix.

Answer 1

$\begin{vmatrix}4&2&3\\0&4&0\\3&8&3\end{vmatrix}$

The second row is the best candidate for cofactor expansion since 2 of the 3 entries are 0. The determinant is then equal to

$0\begin{vmatrix}2&3\\8&3\end{vmatrix}-4\begin{vmatrix}4&3\\3&3\end{vmatrix}+0\begin{vmatrix}4&2\\3&8\end{vmatrix}=-4\begin{vmatrix}4&3\\3&3\end{vmatrix}=-4(12-9)=\boxed{-12}$