Construct a `3xx3` matrix whose elements are given by `a_(ij)={{:((1)/(2)|2i-3j|","i!=j),(|2i-j|","i=j):}`

Explanation

Any `3xx3` matrix is given by `A={:[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))]:}`
Given, `a_(ij)={{:((1)/(2)|2i-3j|","i!=j),(|2i-j|","i=j):}`
Now,
`a_(11)=|2-1|=1`
`a_(12)=(1)/(2)|2-6|=2`
`a_(13)=(1)/(2)|2-9|=(7)/(2)`
`a_(21)=(1)/(2)|4-3|=(1)/(2)`
`a_(22)=|4-2|=2`
`a_(23)=(1)/(2)|4-9|=(5)/(2)`
`a_(31)=(1)/(2)|6-3|=(3)/(2)`
`a_(32)=(1)/(2)|6-6|=0`
`a_(33)=|6-3|=3`
Hence, required matrix is `{:[(1,2,7//2),(1//2,2,5//2),(3//2,0,3)]:}`