Matrix

nanted1

New member
Joined
Jan 30, 2006
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4
Calculate the determinant of the following matrix using Laplace expansion

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

|A|=
 
Hello, nanted1!

Calculate the determinant of the following matrix using Laplace expansion

    A  =  561280132\displaystyle \;\;A\;= \;\begin{vmatrix}5&6&1 \\ 2&8&0 \\ 1&3&2\end{vmatrix}

A  =  5803262012  +  12813\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}

      =  5(160)6(40)+1(68)\displaystyle \;\;\;=\;5(16\,-\,0)\,-\,6(4\,-\,0)\,+\,1(6\,-\,8)

      =  80242\displaystyle \;\;\;=\;80\,-\,24\,-\,2

      =  54\displaystyle \;\;\;=\;54
 
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