Question

Construa a matriz C de ordem 3x3 cuja lei de formação é: *

Answer 1

Resposta:

Opção 1.

Explicação passo a passo:

Matriz $C_{3\times3}$, com $c_{ij}=3i-2j$.

Ilustrando os elementos de uma matriz genérica de ordem 3:

$C=\left[\begin{array}{ccc}c_{11}&c_{12}&c_{12}\\c_{21}&c_{22}&c_{23}\\c_{31}&c_{32}&c_{33}\end{array}\right]$

Calculando os elementos pela fórmula, teremos:

$c_{11}=3\cdot1-2\cdot1=3-2=1\\\\c_{12}=3\cdot1-2\cdot2=3-4=-1\\\\c_{13}=3\cdot1-2\cdot3=3-6=-3\\\\c_{21}=3\cdot2-2\cdot1=6-2=4\\\\c_{22}=3\cdot2-2\cdot2=6-4=2\\\\c_{23}=3\cdot2-2\cdot3=6-6=0\\\\c_{31}=3\cdot3-2\cdot1=9-2=7\\\\c_{32}=3\cdot3-2\cdot2=9-4=5\\\\c_{33}=3\cdot3-2\cdot3=9-6=3$

Portanto:

$C=\left[\begin{array}{ccc}1&-1&-3\\4&2&0\\7&5&3\end{array}\right]$