Question

Calcule os determinantes aplicando a regra de sarrus:

d) |5 0 -1|
|2 3 4|
|1 2 3 |

e) | 1 2 0 |
| 2 4 1 |
|-3 -6 0 |

Answer 1

Caso tenha problemas para visualizar a resposta experimente abrir pelo navegador https://brainly.com.br/tarefa/34972136

                                                       

d)

$\sf\Psi=\begin{vmatrix}\sf5&\sf0&\sf-1\\\sf2&\sf3&\sf4\\\sf1&\sf2&\sf3\end{vmatrix}\begin{vmatrix}\sf5&\sf0\\\sf2&\sf3\\\sf1&\sf2\end{vmatrix}\\\sf det~\Psi=5\cdot3\cdot3+0\cdot4\cdot1+(-1)\cdot2\cdot2-0\cdot2\cdot3-5\cdot4\cdot2-(-1)\cdot3\cdot1\\\sf det~\Psi=45+0-4-0-40+3\\\sf det~\Psi=48-44\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~~ det~\Psi=4}}}}$

e)

$\sf \Phi=\begin{vmatrix}\sf1&\sf2&\sf0\\\sf2&\sf4&\sf1\\\sf-3&\sf-6&\sf0\end{vmatrix}\begin{vmatrix}\sf1&\sf2\\\sf2&\sf4\\\sf-3&\sf-6\end{vmatrix}\\\sf det~\Phi=1\cdot4\cdot0+2\cdot1\cdot(-3)+0\cdot2\cdot(-6)-2\cdot2\cdot0-1\cdot1\cdot(-6)-0\cdot4\cdot(-3)\\\sf det~\Phi=0-6+0-0+6-0\\\huge\boxed{\boxed{\boxed{\boxed{\sf det~\Phi=0}}}}$

Nota:

$\boxed{\begin{array}{c}\sf Se~uma~matriz~possuir~uma~linha~ou~coluna\\\sf proporcional~ent\tilde ao~o~determinante~\acute e~nulo.\end{array}}$

Answer 2

Explicação passo-a-passo:

d)

$\sf A=\Big[\begin{array}{ccc} \sf 5 & \sf 0 & \sf -1 \\ \sf 2 & \sf 3 & \sf 4 \\ \sf 1 & \sf 2 & \sf 3 \end{array}\Big]$

$\sf det~(A)=5\cdot3\cdot3+0\cdot4\cdot1+(-1)\cdot2\cdot2-1\cdot3\cdot(-1)-2\cdot4\cdot5-3\cdot2\cdot0$

$\sf det~(A)=45+0-4+3-40-0$

$\sf det~(A)=48-44$

$\sf \red{det~(A)=4}$

e)

$\sf A=\Big[\begin{array}{ccc} \sf 1 & \sf 2 & \sf 0 \\ \sf 2 & \sf 4 & \sf 1 \\ \sf -3 & \sf -6 & \sf 0 \end{array}\Big]$

$\sf det~(A)=1\cdot4\cdot0+2\cdot1\cdot(-3)+0\cdot2\cdot(-6)-(-3)\cdot4\cdot0-(-6)\cdot1\cdot1-0\cdot2\cdot2$

$\sf det~(A)=0-6-0+0+6-0$

$\sf det~(A)=-6+6$

$\sf \red{det~(A)=0}$