Matrix

[nanted1]

Calculate the determinant of the following matrix using Laplace expansion

A=
| 5 6 1 |
| 2 8 0 |
| 1 3 2 |

|A|=

 

[soroban]

Hello, nanted1!

Calculate the determinant of the following matrix using Laplace expansion

\(\displaystyle \;\;A\;= \;\begin{vmatrix}5&6&1 \\ 2&8&0 \\ 1&3&2\end{vmatrix}\)

\(\displaystyle |A|\;=\;5\begin{vmatrix}8&0\\3&2\end{vmatrix}\,-\,6\begin{vmatrix}2&0\\1&2\end{vmatrix}\;+\;1\begin{vmatrix}2&8\\1&3\end{vmatrix}\)

\(\displaystyle \;\;\;=\;5(16\,-\,0)\,-\,6(4\,-\,0)\,+\,1(6\,-\,8)\)

\(\displaystyle \;\;\;=\;80\,-\,24\,-\,2\)

\(\displaystyle \;\;\;=\;54\)