Question

Considere as matrizes:
A = (aij)2x2, definida por aij = i-j
B = (bij)2x2, definida por bij = i
C = (cij), C = A+B

Qual o elemento C21

a) -1

b) 0

c) 1

d) 2

e) 3

Answer 1

Resposta:

Alternativa e)

Explicação passo a passo:

i = linha e j = coluna

A=(aij)₂ₓ₂, definida por aij = i-j

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

a₁₁=1-1=0

a₁₂=1-2= -1

a₂₁=2-1=1

a₂₂=2-2=0

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

B = (bij)₂ₓ₂, definida por bij = i

$B = \left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]$

b₁₁=1

b₁₂=1

b₂₁=2

b₂₂=2

$B = \left[\begin{array}{ccc}1&1\\2&2\end{array}\right]$$C=A+B= \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]+\left[\begin{array}{ccc}1&1\\2&2\end{array}\right]=\left[\begin{array}{ccc}0+1&-1+1\\1+2&0+2\end{array}\right]=\left[\begin{array}{ccc}1&0\\3&2\end{array}\right]$

c₂₁=3