Question

find the value of each determinant

$\left|\begin{array}{ccc}2& 1& -3\\ 5& 0& 1\\ 2& 6& 0\end{array}\right|$

Short answer

$D=-100$

Step-by-step solution

Step 1. The given information is

$\left|\begin{array}{ccc}2& 1& -3\\ 5& 0& 1\\ 2& 6& 0\end{array}\right|$

Step 2. Using the formula for the determinant D=abcdefghiD=a(ei-fh)-b(di-gf)-c(dh-eg)

$$\begin{gathered} D=\left|\begin{array}{ccc}2& 1& -3\\ 5& 0& 1\\ 2& 6& 0\end{array}\right| \\ D=2(0\times 0-1\times 6)-1(5\times 0-2\times 1)+(-3)(5\times 6-2\times 0) \\ D=2(0-6)-1(0-2)+(-3)(30-0) \\ D=(-12)+2-90 \\ D=-100 \end{gathered}$$