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

Answer

N/a

Explanation

`(i) LetA=[{:(a_(11),a_(12),a_(13),a_(14)),(a_(21),a_(22),a_(23),a_(24)),(a_(31),a_(32),a_(33),a_(34)):}]`
where`A=(1)/(2){-3i-J|`
`therefore a_(11)=(1)/(2){-3xx1+1}=1,`
` a_(12)=(1)/(2){-3xx1+1}=(1)/(2),`
` a_(13)=(1)/(2)|-3xx1+1|=0,`
`A_(14)=(1)/(2)|-3xx1+1|=(1)/(2),`
`a(21)=(1)/(2)|-3xx1+1|==(5)/(2),`
`a_(22)=(1)/(2)|-3xx1+1|=2,`
`a_(23)=(1)/(2)|-3xx1+1|=(3)/(2),`
`a_(24)=(1)/(2)|-3xx1+1|=1,`
`a_(31)=(1)/(2)|-3xx1+1|=4,`
`a_(32)=(1)/(2)|-3xx1+1|=(7)/(2),`
`a_(33)=(1)/(2)|-3xx1+1|=3,`
`a_(34)=(1)/(2)|-3xx1+1|=(5)/(2)`
`therefore A=[{:(1,(1)/(2),0,(1)/(2)),((5)/(2),2,(3)/(2),1),(4,(7)/(2),3,(5)/(2)):}]`
`(ii) Let 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)):}]`
where `a_(ij)=2i-j`
`therefore a_(11)=2xx1-1=1,a_(12)=2xx1-2=0,`
`a_(31)=2xx1-3=-1,a_(14)=2xx1-4=-2,`
`a_(21)=2xx2-1=3,a_(22)=2xx2-4=0,`
`a_(31)=2xx3-1=5, a_(32)=2xx3-2=4,`
`a_(33)=2xx3-3=3, a_(34)=2xx3-4=2`
` therefore A=[{:(1,0,-1,-2),(3,2,1,0),(5,4,3,2):}]`