Let `A=|1sintheta1-sintheta1sintheta-1-sintheta1|,` where `0lt=thetalt=2pidot` Then `D e t(A)=0` (b) `D e t(A) in (2,oo)` `D e t(A) in (2,4)` (d) `D e t(A) in [2,4]`

Explanation

`A=|(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1)|`

`R_{1}+R_{3}`

`A=|(0,0,2),(-sintheta,1,sintheta),(-1,-sintheta,1)|`

`=2(sin ^{2} theta+1)`

`-1 <=sin theta <=1`

`0 <=sin^2 theta<=1`

`1 <=1+sin^2 theta <=2`

`2 <=2(1+sin^2 theta ) <=4`

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