Let A=(aij) and aij=j-i then determine A ?

To determine the matrix A, we need to find the values of aij for all possible values of i and j.

Given that aij = j - i, we can calculate the values of aij as follows:

For i = 1:
a11 = 1 - 1 = 0
a12 = 2 - 1 = 1
a13 = 3 - 1 = 2
...

For i = 2:
a21 = 1 - 2 = -1
a22 = 2 - 2 = 0
a23 = 3 - 2 = 1
...

For i = 3:
a31 = 1 - 3 = -2
a32 = 2 - 3 = -1
a33 = 3 - 3 = 0
...

Continuing this pattern, we can find the values of aij for all possible values of i and j.

The matrix A would be:

A =
| 0 1 2 |
| -1 0 1 |
| -2 -1 0 |