Question -
Answer -
(i) Given (i + j)2 /2
Let A = [ai j]2×2
So, the elements in a 2 × 2 matrix are
a11, a12, a21, a22
a11 = 
a12 =
a21 =
a22 = 
Substituting these values in matrix A we get,
(ii) Given ai j = (i – j)2 /2
Let A = [ai j]2×2
So, the elements in a 2 × 2 matrix are
a11, a12, a21, a22
a11 =
a12 = 
a21 =
a22 =
Substituting these values in matrix A we get,
(iii) Given ai j = (i – 2j)2 /2
Let A = [ai j]2×2
So, the elements in a 2 × 2 matrix are
a11, a12, a21, a22
a11 =
a12 =
a21 =
a22 =
Substituting these values in matrix A we get,
(iv) Given ai j = (2i + j)2 /2
Let A = [ai j]2×2
So, the elements in a 2 × 2 matrix are
a11, a12, a21, a22
a11 =
a12 =
a21 =
a22 =
Substituting these values in matrix A we get,
(v) Given ai j = |2i – 3j|/2
Let A = [ai j]2×2
So, the elements in a 2×2 matrix are
a11, a12, a21, a22
a11 =
a12 =
a21 =
a22 =
Substituting these values in matrix A we get,
(vi) Given ai j = |-3i + j|/2
Let A = [ai j]2×2
So, the elements in a 2 × 2 matrix are
a11, a12, a21, a22
a11 =
a12 =
a21 =
a22 =
Substituting these values in matrix A we get,
(vii) Given ai j = e2ix sin x j
Let A = [ai j]2×2
So, the elements in a 2 × 2 matrix are
a11, a12, a21, a22,
a11 =
a12 =
a21 =
a22 =
Substituting these values in matrix A we get,
a33 =
a34 =
Substituting these values in matrix A we get,
A =
Multiplying by negative sign we get,