Question

É urgente pfvr!!
Dada as matrizes A = (aij) 2x3 com aij = mmc(i;j) e B = (bij) 2x3 com bij = mdc(i;j), obtenha a matriz resultante de A +B.

Answer 1

Explicação passo-a-passo:

$A=\left(\begin{array}{ccc} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \end{array}\right)$

$a_{11}=\text{mmc}(1,1)~\longrightarrow~a_{11}=1$

$a_{12}=\text{mmc}(1,2)~\longrightarrow~a_{12}=2$

$a_{13}=\text{mmc}(1,3)~\longrightarrow~a_{13}=3$

$a_{21}=\text{mmc}(2,1)~\longrightarrow~a_{21}=2$

$a_{22}=\text{mmc}(2,2)~\longrightarrow~a_{22}=2$

$a_{23}=\text{mmc}(2,3)~\longrightarrow~a_{23}=6$

$A=\left(\begin{array}{ccc} 1&2&3 \\ 2&2&6 \end{array}\right)$

$B=\left(\begin{array}{ccc} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \end{array}\right)$

$a_{11}=\text{mdc}(1,1)~\longrightarrow~a_{11}=1$

$a_{12}=\text{mdc}(1,2)~\longrightarrow~a_{12}=1$

$a_{13}=\text{mdc}(1,3)~\longrightarrow~a_{13}=1$

$a_{21}=\text{mdc}(2,1)~\longrightarrow~a_{21}=1$

$a_{22}=\text{mdc}(2,2)~\longrightarrow~a_{22}=2$

$a_{23}=\text{mdc}(2,3)~\longrightarrow~a_{23}=1$

$B=\left(\begin{array}{ccc} 1&1&1 \\ 1&2&1 \end{array}\right)$

$A+B=\left(\begin{array}{ccc} 1&2&3 \\ 2&2&6 \end{array}\right)+\left(\begin{array}{ccc} 1&1&1 \\ 1&2&1 \end{array}\right)$

$A+B=\left(\begin{array}{ccc} 1+1&2+1&3+1 \\ 2+1&2+2&6+1 \end{array}\right)$

$A+B=\left(\begin{array}{ccc} 2&3&4 \\ 3&4&7 \end{array}\right)$