Question

seja a matriz A= (AIJ)5X5 TAL QUE AIJ= 6I - 2J DETERMINE A SOMA DOS ELEMENTOS DA DIAGONAL PRINCIPAL DA MATRIZ ajuda pfvv

Answer 1

Explicação passo-a-passo:

$\sf a_{ij}=6i-2j$

$\sf a_{11}=6\cdot1-2\cdot1\Rightarrow a_{11}=6-2\Rightarrow a_{11}=4$

$\sf a_{22}=6\cdot2-2\cdot2 \Rightarrow a_{22}=12-4~\Rightarrow~a_{22}=8$

$\sf a_{33}=6\cdot3-2\cdot3\Rightarrow a_{33}=18-6\Rightarrow a_{33}=12$

$\sf a_{44}=6\cdot4-2\cdot4\Rightarrow a_{44}=24-8~\Rightarrow~a_{44}=16$

$\sf a_{55}=6\cdot5-2\cdot5\Rightarrow a_{55}=30-10\Rightarrow a_{55}=20$

A soma dos elementos da diagonal principal é:

$\sf a_{11}+a_{22}+a_{33}+a_{44}+a_{55}=4+8+12+16+20$

$\sf \red{a_{11}+a_{22}+a_{33}+a_{44}+a_{55}=60}$