Question

write the matrix with elements aij = 2i + j, i, j=1, 2,3​

Answer 1

Given : a matrix with elements aij=2i + j, i, j =1, 2,3​

To Find :  Matrix

Solution:

aij=2i + j

a₁₁ = 2(1) + 1  = 3

a₁₂ = 2(1) + 2  = 4

a₁₃ = 2(1) + 3  = 5

a₂₁ = 2(2) + 1  = 5

a₂₂ = 2(2) + 2  = 6

a₂₃ = 2(2) + 3  = 7

a₃₁ = 2(3) + 1  = 7

a₃₂ = 2(3) + 2  = 8

a₃₃ = 2(3) + 3  = 9

Matrix is :

$\left[\begin{array}{ccc}3&4&5\\5&6&7\\7&8&9\end{array}\right]$

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Answer 2

To find :-

• The matrix

Solution :-

Given:-

$\implies$ aij=2i + j

So,

$\implies$a₁₁ = 2(1) + 1 = 3

$\implies$a₁₂ = 2(1) + 2 = 4

$\implies$a₁₃ = 2(1) + 3 = 5

$\implies$a₂₁ = 2(2) + 1 = 5

$\implies$a₂₂ = 2(2) + 2 = 6

$\implies$a₂₃ = 2(2) + 3 = 7

$\implies$a₃₁ = 2(3) + 1 = 7

$\implies$a₃₂ = 2(3) + 2 = 8

$\implies$a₃₃ = 2(3) + 3 = 9

[Note - Matrix is given in the attachment]