Question

Seja ai j a representação de um elemento de uma matriz na linha i e coluna j, escreva as matrizes a seguir:
a) A=(aij)2x3,onde aij =2i+3j
b) B= (bij)3x3 ,onde bij = ij
c) C=(cij)4x1,ondecij =i2 +j
d) D=(dij)1x3,ondedij =i–j
e) E = ( ei j) , onde ei j = { 2, se i ≥ j 4 x 3 –1, se i < j

Answer 1

espero que ajude. não consigo colocar a resolução pq fiz a lápis e seria muita coisa pra escrever

Answer 2

• O que é uma matriz?

É uma tabela organizada em linhas e colunas no formato $\bold{m~x~n}$, onde

• m representa o número de linhas
• n representa o número de colunas

Cada elemento da matriz é identificado por seus índices. Por exemplo, o elemento $\bold{a_{34} }$ é o elemento da matriz A, localizado na linha 3, coluna 4.

• Resolvendo o problema

Segundo o enunciado, temos

$a)~A=(a_{ij})_{2\times3},~~~\text{onde}~~~a_{ij}=2i+3j\\\\\\a_{11}=2~.~1+3~.~1=2+3=5\\a_{12}=2~.~1+3~.~2=2+6=8\\a_{13}=2~.~1+3~.~3=2+9=11\\\\a_{21}=2~.~2+3~.~1=4+3=7\\a_{22}=2~.~2+3~.~2=4+6=10\\a_{23}=2~.~2+3~.~3=4+9=13\\\\\\A=\left[\begin{array}{ccc}5&8&11\\7&10&13\end{array}\right]$

$\hrulefill\\\\b)~B=(b_{ij})_{3\times3},~~~\text{onde}~~~b_{ij}=\dfrac{i}{j}\\\\\\b_{11}=\frac{1}{1}=1\\\\b_{12}=\frac{1}{2}\\\\b_{13}=\frac{1}{3}\\\\\\b_{21}=\frac{2}{1}=2\\\\b_{22}=\frac{2}{2}=1\\\\b_{23}=\frac{2}{3}\\\\\\b_{31}=\frac{3}{1}=3\\\\b_{32}=\frac{3}{2}\\\\b_{33}=\frac{3}{3}=1\\\\\\\\B=\left[\begin{array}{ccc}1&\frac{1}{2}&\frac{1}{3}\\\\2&1&\frac{2}{3}\\\\3&\frac{3}{2}&1\end{array}\right]$

$\hrulefill\\\\c)~C=(c_{ij})_{4\times1},~~~\text{onde}~~~c_{ij}=i^2 +j\\\\\\c_{11}=1^2 +1=1+1=2\\\\c_{21}=2^2 +1=4+1=5\\\\c_{31}=3^2 +1=9+1=10\\\\c_{41}=4^2 +1=16+1=17\\\\\\\\C=\left[\begin{array}{c}2\\5\\10\\17\end{array}\right]$

$\hrulefill\\\\d)~D=(d_{ij})_{1\times3},~~~\text{onde}~~~d_{ij}=i-j\\\\d_{11}=1-1=0\\\\d_{12}=1-2=-1\\\\d_{13}=1-3=-2\\\\d_{14}=1-4=-3\\\\D=\left[\begin{array}{clcl}0&-1&-2&-3\end{array}\right]$

$\hrulefill\\\\e)~E=(e_{ij})_{4\times3},~~~\text{onde}~~~e_{ij}=\left \{ {{{~2,~se~i~\geq~j} \atop {-1,~se~i~<~j}} \right.\\\\e_{11}=2\\e_{12}=-1\\e_{13}=-1\\\\e_{21}=2\\e_{22}=2\\e_{23}=-1\\\\e_{31}=2\\e_{32}=2\\e_{33}=2\\\\e_{41}=2\\e_{42}=2\\e_{43}=2\\\\\\E=\left[\begin{array}{ccc}2&-1&-1\\2&2&-1\\2&2&2\\2&2&2\end{array}\right]$

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