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KCET2022MathematicsDeterminants

If A_n= [ array cc 1-n & n n & 1-n array ] , then |A₁ |+ |A₂ |+ |A₂₀₂₁ |=

Options

  1. A-2021
  2. B-(2021)^2
  3. C(2021)^2
  4. D4042

Correct answer

B. -(2021)^2

Step-by-step solution

Given, A_n= [ array cc 1-n & n n & 1-n array ] and aligned & |A_n |= [ array cc 1-n & n n & 1-n array ] & =(1-n)^2-n^2=1+n^2-2 n-n^2 & |A_n |=1-2 n & Now. |A₁ |+ |A₂ |+ |A₃ |+ .+ |A₂₀₂₁ | & =(1-2)+(1-4)+(1-6)+ +(1-4042) & =(1+1+ .+1)-(2+4+6+ .+4042) & =2021- [ 2021 2 (2+4042) ] & =2021- 2021 2 4044=2021-2021 2022 & =2021(1-2022)=-(2021)^2 & aligned

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