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

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)

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

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

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

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

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