Question

Construa a matriz A = ( aij ) do tipo 2x3, sendo aij =3i^2 – j^2 *
a- 210
543

B 210
540

C 210
533

D 210
573

Answer 1

assinala a que aparece isso:

$\large{ \bold{ \red{A = \left( \begin{array}{ccc}2&-1& - 6\\11&8&3\end{array} \right)}}}$

.....

EXPLICACÃO:

se essa matriz A = (aij) tem tipo 2×3 entao ela tem tem 2 linhas e 3 colunas. montando esta matriz A genérica:

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

agora aplicando a definiçao dada para estes elementos:

$a_{ij }=3i^2 – j^2$

$\small{a_{11 }=3.(1)^2 – 1^2 = 3.1 - 1 = 3 - 1 = \bold{ \red{ 2}}}$

$\small{a_{12 }=3.(1)^2 – 2^2 = 3.1 - 4 = 3 - 4 = \red{ \bold{-1}}}$

$\small{a_{13 }=3.(1)^2 – 3^2 = 3.1 - 9 = 3 - 9 = \red{ \bold{ - 6}}}$

$\small{a_{21 }=3.(2)^2 – 1^2 = 3.4 - 1 = 12 - 1 = \red{ \bold{11}}}$

$\small{a_{22 }=3.(2)^2 – 2^2 = 3.4 - 4 = 12- 4 = \red{ \bold{8}}}$

$\small{a_{23 }=3.(2)^2 – 3^2 = 3.4 - 9 = 12 - 9= \red{ \bold{3}}}$

colocando estes resultados nos seus lugares na matriz genérica A :

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

$\large{ \bold{ \red{A = \left( \begin{array}{ccc}2&-1& - 6\\11&8&3\end{array} \right)}}}$

Answer 2

$A=\left(a_{ij}\right)_{2\times3}\ | \ a_{ij}=3i^2-j^2\Longrightarrow A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{array}\right]$

$a_{11}=3(1)^2-(1)^2=3-1\ \therefore\ a_{11}=2$

$a_{12}=3(1)^2-(2)^2=3-4\ \therefore\ a_{12}=-1$

$a_{13}=3(1)^2-(3)^2=3-9\ \therefore\ a_{13}=-6$

$a_{21}=3(2)^2-(1)^2=12-1\ \therefore\ a_{21}=11$

$a_{22}=3(2)^2-(2)^2=12-4\ \therefore\ a_{22}=8$

$a_{23}=3(2)^2-(3)^2=12-9\ \therefore\ a_{23}=3$

$A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{array}\right] \Longrightarrow \boxed{A=\left[\begin{array}{ccc}2&-1&-6\\11&8&3\end{array}\right] }$