Question

construa matrizes a partir das representações

Answer 1

Resposta:

Olá!

Explicação passo-a-passo:

1. a) $a_{ij}=i^2+j$

Matriz 2x3

$\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\\end{array}\right]$

$a_{11}=1^2+1=1+1=2$

$a_{12}=1^2+2=1+2=3$

$a_{13}=1^2+3=1+3=4$

$a_{21}=2^2+1=4+1=5$

$a_{22}=2^2+2=4+2=6$

$a_{23}=2^2+3=4+3=7$

$A=\left[\begin{array}{ccc}2&3&4\\5&6&7\\\end{array}\right]$

b) $b_{ij}=\left \{ {{i+j , i=j} \atop {2i-j, i\neq j}} \right.$

Matriz 3x3

$\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right]$

$a_{11}=1+1=2$

$a_{12}=2.1-2=2-2=0$

$a_{13}=2.1-3=2-3=-1$

$a_{21}=2.2-1=4-1=3$

$a_{22}=2+2=4$

$a_{23}=2.2-3=4-3=1$

$a_{31}=2.3-1=6-1=5$

$a_{32}=2.3-2=6-2=4$

$a_{33}=3+3=6$

$B=\left[\begin{array}{ccc}2&0&-1\\3&4&1\\5&4&6\end{array}\right]$

Bons Estudos!