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Prove that : |{:(a+b,b+c,c+a),(b+c,c+a...

Prove that :
`|{:(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|`.

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MODERN PUBLICATION-DETERMINANTS-FREQUENTLY ASKED QUESTIONS
  1. The maximum value of |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)| is 1/...

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  2. Using properties of determinants prove that ((1,1, 1+3x),(1+3y,1,1),(...

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  3. If Delta=|{:(1,a,a^(2)),(a,a^(2),1),(a^(2),1,a):}|=-4, then find the v...

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  4. Prove that : |{:(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c):}|=2|{:(a,...

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  5. |[b^2c^2,bc,b+c] , [c^2a^2,ca,c+a] , [a^2b^2,ab,a+b]|=0

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  6. Without expanding, prove that the following determinants vanish : |{...

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  7. If f(x)|a-1 0a x a-1a x^2a x a|, using properties of determinants, fin...

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  8. Using properties of determinants , find the value of k if |{:(x,y,x+...

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  9. Prove that : |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^(...

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  10. If x,y,z are different and Delta=|{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)...

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  11. Prove that : |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+(1)/(a)+(1)/(...

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  12. Show that |[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(b-c)(c-a)(a-b)(bc+ca...

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  13. Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a...

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  14. Prove that |y z-x^2z x-y^2x y-z^2z x-y^2x y-z^2y z-x^2x y-z^2y z-x^2z ...

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

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  16. |[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=

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  17. Using properties of determinants, prove that : |{:((x+y)^(2),zx,xy),...

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