Construct a 2 × 2 matrix A = [\( a_{i j}\)] whose elements \( a_{i j}\) are given by: \(\dfrac{ (i + j)^2} {2}\)

Given \(\dfrac{ (i + j)^2 }{2}\)

Let A = [a_{i j}]_{2×2}

So, the elements in a 2 × 2 matrix are

a_{11}, a_{12}, a_{21}, a_{22}

a_{11 }=2_{ }

a_{12 }= 4.5

a_{21 }= 4.5

a_{22 }= 8

Substituting these values in matrix A we get,

Find the values of a, b, c and d from the equations:

Find x, y, a and b if

Construct a 4 × 3 matrix A = [a_{i j}] whose elements a_{i j} are given by a_{i j} = i

Construct a 4 × 3 matrix A = [ai j] whose elements ai j are given by \( a_{i j} = \dfrac{(i – j)}{(i + j)}\)