Question

Seja A=(aij)3x3, com aij=i+j, e B=(bij)3x3, com bij=2i-j, determine a matriz A e a matriz B.

Answer 1

$\left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right]$

Montando a matriz A:
aij=i+j
a11=1+1=2
a12=1+2=3
a13=1+3=4
a21=2+1=3
a22=4
a23=5
a31=4
a32=5
a33=6

A=$\left[\begin{array}{ccc}2&3&4\\3&4&5\\4&5&6\end{array}\right]$

Montando a matriz B:
bil=2i-j
b11=2(1)-1=1
b12=2(1)-2=0
b13=-1
b21=3
b22=2
b23=1
b31=5
b32=4
b33=3

B=$\left[\begin{array}{ccc}1&0&-1\\3&2&1\\5&4&3\end{array}\right]$

Answer 2

Boa tarde

uma matriz 3x3 tem 3 linhas (i) e 3 culnas (j)

aij = i + j

A(1,1) = 1 + 1 = 2
A(1,2) = 1 + 2 = 3
A(1,3) = 1 + 3 = 4

A(2,1) = 2 + 1 = 3
A(2,2) = 2 + 2 = 4
A(2,3) = 2 + 3 = 5

A(3,1) = 3 + 1 = 4
A(3,2) = 3 + 2 = 5
A(3,3) = 3 + 3 = 6

bij = 2i - j

B(1,1) = 2*1 - 1 = 1
B(1,2) = 2*1 - 2 = 0
B(1,3) = 2*1 - 3 = -1

B(2,1) = 2*2 - 1 = 3
B(2,2) = 2*2 - 2 = 2
B(2,3) = 2*2 - 3 = 1

B(3,1) = 2*3 - 1 = 5
B(3,2) = 2*3 - 2 = 4
B(3,3) = 2*3 - 3 = 3