Using properties of determinants, prove that 3 2 (a 1) 3 3 1 2a 1 a 2 1 a 2a 2a

Answer

N/a

Explanation

We have to prove
`=|(a^(2)+2a,2a+1,1),(2a+1,a+2,1),(3,3,1)|`
`=|(a^(2)+2a-2a-1, 2a+1-a-2,0),(2a+1-3,a+2-3,0),(3,3,1)|`
`[ :' R_(1)toR_(1)-R_(2)` and `R_(2)toR_(2)-R_(3)]`
`=|((a-1)(a+1),(a-1),0),(2(a-1),(a-1),0),(3,3,1)|=(a-1)^(2)|((a+1),1,0),(2,1,0),(3,3,1)|`
[taking`(a-1)` common from `R_(1)` and `R_(2)` each]
`(a-1)^(2)[1(a+1)-2]-(a-1)^(3)`
`=RHS` Hence proved