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Appropriately matching the information given in the three columns of the following table. Column 1Column 2Column 3(I)If a, b, c ϵR−{0} such that a≠b≠cand 1a+1b+1c=0 and A=⎡⎢⎣1+a1111+b1111+c⎤⎥⎦,then(i)A is singular matrix(P)|adj A|=|A|2(II)If α, β, γ ϵ R, andA=⎡⎢⎣1cos(α−β)cos(α−γ)cos(β−α)1cos(β−γ)cos(γ−α)cos(γ−β)1⎤⎥⎦,then(ii)A is singular matrix(Q)adj(adj A)=|A|A(III)If ω≠1 be cube root of unity and(iii)A is non-singular matrix(R)|A| is equal toA=⎡⎢⎣1+2ω100+ω200ω2111+ω101+2ω202ωωω22+ω100+2ω200⎤⎥⎦is equal to minimum value of,thencos−1(x−1x)+cos−1(y2y+1)+cos−1(z2+z+1)(where x, y, z are real numbers)(IV)If a, b, c ϵR−{0} such that a≠b≠c,andA=⎡⎢⎢⎣0(a−b)3(a−c)3(b−a)30(b−c)3(c−a)3(c−b)30⎤⎥⎥⎦,then(iv)Invertible(S)|A−1|=1|A| Which of the following is only correct combination ? |
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Answer» Appropriately matching the information given in the three columns of the following table. Column 1Column 2Column 3(I)If a, b, c ϵR−{0} such that a≠b≠cand 1a+1b+1c=0 and A=⎡⎢⎣1+a1111+b1111+c⎤⎥⎦,then(i)A is singular matrix(P)|adj A|=|A|2(II)If α, β, γ ϵ R, andA=⎡⎢⎣1cos(α−β)cos(α−γ)cos(β−α)1cos(β−γ)cos(γ−α)cos(γ−β)1⎤⎥⎦,then(ii)A is singular matrix(Q)adj(adj A)=|A|A(III)If ω≠1 be cube root of unity and(iii)A is non-singular matrix(R)|A| is equal toA=⎡⎢⎣1+2ω100+ω200ω2111+ω101+2ω202ωωω22+ω100+2ω200⎤⎥⎦is equal to minimum value of,thencos−1(x−1x)+cos−1(y2y+1)+cos−1(z2+z+1)(where x, y, z are real numbers)(IV)If a, b, c ϵR−{0} such that a≠b≠c,andA=⎡⎢ Which of the following is only correct combination ? |
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