Question -
Answer -
(i) Given ai j = i × j
Let A = [ai j]2 × 3
So, the elements in a 2 × 3 matrix are
[a11, a12,a13, a21, a22, a23]
a11 = 1 × 1 = 1
a12 = 1 × 2 = 2
a13 = 1 × 3 = 3
a21 = 2 × 1 = 2
a22 = 2 × 2 = 4
a23 = 2 × 3 = 6
Substituting these values in matrix A we get,
(ii) Given ai j = 2i – j
Let A = [ai j]2×3
So, the elements in a 2 × 3 matrix are
a11, a12, a13, a21,a22, a23
a11 = 2 × 1 – 1 = 2 – 1 = 1
a12 = 2 × 1 – 2 = 2 – 2 = 0
a13 = 2 × 1 – 3 = 2 – 3 = – 1
a21 = 2 × 2 – 1 = 4 – 1 = 3
a22 = 2 × 2 – 2 = 4 – 2 = 2
a23 = 2 × 2 – 3 = 4 – 3 = 1
Substituting these values in matrix A we get,
(iii) Given ai j = i + j
Let A = [a i j] 2×3
So, the elements in a 2 × 3 matrix are
a11, a12, a13, a21,a22, a23
a11 = 1 + 1 = 2
a12 = 1 + 2 = 3
a13 = 1 + 3 = 4
a21 = 2 + 1 = 3
a22 = 2 + 2 = 4
a23 = 2 + 3 = 5
Substituting these values in matrix A we get,
(iv) Given ai j = (i + j)2/2
Let A = [ai j]2×3
So, the elements in a 2 × 3 matrix are
a11, a12, a13, a21,a22, a23
Let A = [ai j]2×3
So, the elements in a 2 × 3 matrix are
a11, a12, a13, a21,a22, a23
a11 =
a12 = 
a13 = 
a21 = 
a22 = 
a23 = 
Substituting these values in matrix A we get,
