Construct a `3 xx 4` matrix, whose elements are given by: `a_(i j)=1/2|-3i+j|`

Answer

`[(1,1/2,0,1/2),(5/2,2,3/2,1),(4,7/2,3,5/2)]`

Explanation

A `3xx4` matrix is given by `A=[(a_(11),a_(12),a_(13),a_(14)),(a_(21),a_(22),a_(23),a_(24)),(a_(31),a_(32),a_(33),a_(34))]`
`a_("ij")=1/2 |-3i+j|, i=1, 2, 3` and `j=1, 2, 3, 4`
`:. a_(11)=1/2 |-3xx1+1|=1/2 |-3+1|=1/2|-2|=2/2=1`
`a_(21)=1/2|-3xx2+1|=1/2 |-6+1|=1/2|-5|=5/2`
`a_(31)=1/2|-3xx3+1|=1/2|-9+1|=1/2|-8|=8/2=4`
`a_(12)=1/2 |-3xx1+2|=1/2|-3+2|=1/2 |-1|=1/2`
`a_(22)=1/2 |-3xx2+2|=1/2|-6+2|=1/2 |-4|=4/2=2`
`a_(32)=1/2 |-3xx3+2|=1/2 |-9+2|=1/2 |-7|=7/2`
`a_(13)=1/2 |-3xx1+3|=1/2 |-3+3|=0`
`a_(23)=1/2 |-3xx2+3|=1/2 |-6+3|=1/2|-3|=3/2`
`a_(33)=1/2|-3xx3+3|=1/2|-9+3|=1/2 |-6|=6/2=3`
`a_(14)=1/2 |-3xx1+4|=1/2 |-3+4|=1/2 |1|=1/2`
`a_(24)=1/2 |-3xx2+4|=1/2 |-6+4|=1/2 |-2|=2/2=1`
`a_(34)=1/2 |-3xx3+4|=1/2 |-9+4|=1/2 |-5|=5/2`
Therefore, the required matrix is `A=[(1,1/2,0,1/2),(5/2,2,3/2,1),(4,7/2,3,5/2)]`