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Prove that identities: |[-bc,b^2+bc,c^2...

Prove that identities: `|[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=(a b+b c+a c)^3`

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|[-bc, b^2+bc, c^2 +bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=64 . then (ab+bc+ac) is

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Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

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Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]| is divisible by a+b+c and find the quotient.

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove the identity: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2...

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  2. |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A)...

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  3. Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+...

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  4. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  5. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

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  6. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

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  7. If A(x1, y1),B(x2, y2) and C(x3,y3) are vertices of an equilateral ...

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  8. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

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  9. Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[...

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  10. Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x,...

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  11. Without expanding, show that the value of each of the determinants is ...

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  12. Without expanding, show that the value of each of the determinants is ...

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  13. Without expanding, show that the value of each of the determinants is ...

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  14. Without expanding, show that the value of each of the determinants is ...

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  15. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  16. Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+...

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  17. For any triangleABC, the value of determinant |[sin^2A,cotA,1],[sin^2B...

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  18. Without expanding, show that the value of each of the determinants is ...

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  19. If x , y in R , then the determinant =|(cos x , -sin x,1),(sin x, cos...

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  20. The maximum value of Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)...

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