एक `2xx2` आव्यूह की रचना कीजिए जिसके अवयव निम्नलिखित प्रकार से प्रदत्त हैं :
(i) `a_(ij)=((i+j)^(2))/(2)`
(ii) `a_(ij)=(i)/(j)`
(iii) `a_(ij)=((i+2j)^(2))/(2)`

Explanation

(i) माना `A=[{:(a_(11),a_(12)),(a_(21),a_(22)):}]`
जहाँ `a_(ij)=((I+j)^(2))/(2)`
`thereforea_(11)=((1+1)^(2))/(2)=2,a_(12)=((1+2)^(2))/(2)=(9)/(2)`
`a_(21)=((2+1)^(2))/(2)=(9)/(2),a_(22)=((2+2)^(2))/(2)=8`
`thereforeA=[{:(2,(9)/(2)),((9)/(2),8)]`
(ii) माना `A=[{:(a_(11),a_(12)),(a_(21),a_(22)):}]`
जहाँ `a_(ij)=(i)/(j)`.
`thereforea_(11)=(1)/(1)=1," " a_(12)=(1)/(2)`
`a_(21)=(2)/(1)=2, " "a_(22)=(2)/(2)=1`
`thereforeA=[{:(1,(1)/(2)),(2,1):}]`
(iii) माना `A=[{:(a_(11),a_(12)),(a_(21),a_(22)):}]`
जहाँ `a_(ij)=((i+2j)^(2))/(2)`
`thereforea_(11)=((1+2xx1)^(2))/(2)=(9)/(2),a_(12)=((1+2xx2)^(2))/(2)=(25)/(2)`
`a_(21)=((2+2xx1)^(2))/(2)=8,a_(22)=((2+2xx2)^(2))/(2)=18`
`thereforeA=[{:((9)/(2),(25)/(2)),(8,18):}]`