Question

Construct a 2 × 2 matrix whose elements a_ij are given by:

`a_(ij)=(i-2_j)^2/2`

Answer 1

`a_(ij)=(i-2_j)^2/2`

Here,

`a_11=[1-2(1)]^2/2=(1-2)^2/2=(-1)^2/2=1/2  `,

`a_12=[1-2(2)]^2/2=(1-4)^2/2=(-3)^2/2=9/2`

`a_21= [2-2(1)]^2/2=(2-2)^2/2=0/2=0   ,`

`a_22=[2-2(2)]^2/2=(2-4)^2/2=(-2)^2/2=4/2=2`

 So, the required matrix is `[[1/2  9/2],[0  2]]`