Question

Construa a matriz B=(bij)4x3,tal que bij=i-j².

Answer 1

A matriz será:

0    -3    -8
1    -2    -7
2    -1    -6
3     0    -5

Answer 2

A matriz B=(bij)4x3, possui 4 linhas (horizontais) e 3 colunas (verticais):

$B= \left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\\b_{41}&b_{42}&b_{43}\end{array}\right]$

Sabemos que bij=i-j², então:

$b_{11}=1-1^2=1-1=0 \\ b_{12}=1-2^2=1-4=-3 \\ b_{13}=1-3^2=1-9=-8 \\ b_{21}=2-1^2=2-1=1 \\ b_{22}=2-2^2=2-4=-2 \\ b_{23}=2-3^2=2-9=-7 \\ b_{31}=3-1^2=3-1=2 \\ b_{32}=3-2^2=3-4=-1 \\ b_{33}=3-3^2=3-9=-6 \\ b_{41}=4-1^2=4-1=3 \\ b_{42}=4-2^2=4-4=0 \\ b_{43}=4-3^2=4-9=-5$

Sendo assim, temos a matriz:

$B= \left[\begin{array}{ccc}0&-3&-8\\1&-2&-7\\2&-1&-6\\3&0&-5\end{array}\right]$

:))