Question

Construa as seguintes matrizes:
a) A = (aij)2x3 tal que aij = 3i – j.

Answer 1

Resposta e explicação passo a passo:

Antes das resoluções, vale lembrar que i representa a linha e j representa a coluna de determinado termo a ou b.

a) A = (aij)₂ₓ₃ tal que aij = 3i - j

$A_{2x3}=\left[\begin{array}{ccc}a_{11}&a__{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{array}\right]= \left[\begin{array}{ccc}(3*1-1)&(3*1-2)&(3*1-3)\\(3*2-1)&(3*2-2)&(3*2-3)\end{array}\right]\\\\\\=\left[\begin{array}{ccc}(3-1)&(3-2)&(3-3)\\(6-1)&(6-2)&(6-3)\end{array}\right] =\left[\begin{array}{ccc}2&1&0\\5&4&3\end{array}\right]$

b) B = (bij)₃ₓ₃ tal que bij =

• i + 2j, se i ≠ j
• i - 3j, se i = j

$B_{3X3}=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right] =\left[\begin{array}{ccc}(1-3*1)&(1+2*2)&(1+2*3)\\(2+2*1)&(2-3*2)&(2+2*3)\\(3+2*1)&(3+2*2)&(3-3*3)\end{array}\right] \\\\\\=\left[\begin{array}{ccc}(1-3)&(1+4)&(1+6)\\(2+2)&(2-6)&(2+6)\\(3+2)&(3+4)&(3-9)\end{array}\right] =\left[\begin{array}{ccc}-2&5&7\\4&-4&8\\5&7&-6\end{array}\right]$