Question

Dada a matriz A=(aij)2x2 ,aonde A=i+j;B=(bij)2x3,aonde B= i-j. Responda

A) encontre a matriz A e a matriz B


B)calcule a.b

Answer 1

BNHAcademia ✌

Matriz A

$A_{ij} = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right]$

a₁₁ = 1 + 1 = 2  

a₁₂ = 1 + 2 = 3

a₂₁ = 2 + 1 = 3

a₂₂ = 2 + 2 = 4

$A_{ij} = \left[\begin{array}{ccc}2&3\\3&4\\\end{array}\right]$

Matriz B

$B_{ij} = \left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\\end{array}\right]$

b₁₁ = 1 - 1 = 0

b₁₂ = 1 - 2 = - 1

b₁₃ = 1 - 3 = - 2

b₂₁ = 2 - 1 = 1

b₂₂ = 2 - 2 = 0

b₂₃ = 2 - 3 = - 1

$B_{ij} = \left[\begin{array}{ccc}0&-1&-2\\1&0&-1\\\end{array}\right]$

b) A. B

$A.B =  \left[\begin{array}{ccc}2&3\\3&4\\\end{array}\right]_{2x2}*\left[\begin{array}{ccc}0&-1&-2\\1&0&-1\\\end{array}\right]_{2x3} \\ \\ \\ \\ A.B = \left[\begin{array}{ccc}2.0 + 3.1&2.(- 1)+ 3.0&2.(-2)+3.(-1)\\3.0 + 4.1&3.(-1)+ 4.0&3.(-2)+4.(- 1)\\\end{array}\right] _{2x3} \\ \\ \\ \\ A.B = \left[\begin{array}{ccc}3&-2&-7\\4&- 3&-10\\\end{array}\right]$

Espero ter Colaborado , PLUS ULTRA  xD