Question

Construa as seguintes matrizes:
B=(bij)3x3 tal que bij={i+2j,sei#j{i-3j,se i=j

Answer 1

EAE MANO,

para construir uma matriz de 3a ordem, podemos escrever a sua matriz genérica..

$B= \left(\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right)$

Se i≠j ⇔ i+2j, e i=j ⇔ i-3j, podemos então obter B..

$B= \left(\begin{array}{ccc}i-3j&i+2j&1+2j\\i+2j&i-3j&i+2j\\i+2j&i+2j&i-3j\end{array}\right)\\\\\\ B= \left(\begin{array}{ccc}1-3\cdot1&1+2\cdot2&1+2\cdot3\\2+2\cdot1&2-3\cdot2&2+2\cdot3\\3+2\cdot1&3+2\cdot2&3-3\cdot3\end{array}\right)\\\\\\ \Large\boxed{B= \left(\begin{array}{ccc}-2&5&7\\4&-2&8\\5&7&-3\end{array}\right)}$

Tenha ótimos estudos ;D