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|(a^(2)+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^...

`|(a^(2)+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|= 1 + a^2 + b^2 + c^2`.

Answer

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Prove that |(-a^2,ab,ac),(bc,-b^2,bc),(ca,cb,-c^2)|=4a^(2)b^(2) c^(2) .

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Knowledge Check

  • If |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|=lamdaa^2b^2c^2 then the value of lamda is :

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  • If A = [(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2))] and B = [(0,c,-b),(-c , 0,a),(b,-a,0)] then the product AB equals :

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  • If a^2+b^2+c^2=0 and |(b^2+c^2,ab,ac),(ab,c^2+a^2,bc),(ac,bc,a^2+b^2)|=ka^2b^2c^2 , then the value of k is :

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    Prove that abs{:(a^(2) + 1, ab , ac),(ab, b^(2) + 1, bc),(ca, cb, c^(2) +1):}=1 + a^(2) + b^(2) +c^(2)

    (a) Prove that int_(0)^(2x) f(x) dx = 2int_(0)^(2x) f(x) dx when f(2a-x) =f(x) and hence evaluate int_(0)^(pi) |cos x| dx . (b) Prove that |{:(-a^(2),ab,ac),(bc,-b^(2),bc),(ca,cb,-c^(2)):}|=4a^(2)b^(2)c^(2) .

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