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The determinant |a2\ a^2-(b-c)^2b c b^2b...

The determinant `|a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a b|` is divisible by- a.`a+b+c` b. `(a+b)(b+c)(c+a)` c.`a^2+b^2+c^2` d. `(a-b)(b-c)(c-a)`

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

Show that |[a^2,a^2-(b-c)^2,bc],[b^2,b^2-(c-a)^2,ca],[c^2,c^2-(a-b)^2,ab]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(a-b)^2, ab]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove that |{:(a^(2), a^(2)-(b-c)^(2), bc), (b^(2), b^(2)-(c-a)^(2), ca), (c^(2), c^(2)-(a-b)^(2), ab):}|= (a^(2)+b^(2)+c^(2))(a-b)(b-c)(c-a)(a+b+c)

Find the factor of determinant |(a, b+c, a^2), (b, c+a, b^2), (c, a+b, c^2)|.

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a)(a+b+c)

ALLEN-DETERMINANTS-All Questions
  1. If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y + z =...

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  2. If f^(prime)(x)=|m x m x-p m x+p nn+p n-p m x+2n m x+2n+p m x+2n-p| , ...

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  3. The determinant |a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a ...

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  4. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  5. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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  6. If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  7. If |a a x m m m b x b|=0,\ then x may be equal to- a.a b. b c.a+b d. ...

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  8. The value of the determinant |alphabetalalphax nalphabetax| is indepen...

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  9. If the determinant |a+p l+x u+fb+q x+y v+gc+r n+z w+h| splits into exa...

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  10. The values of lambda for which the system of euations x+y+z=6, x+2y+3z...

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  11. If x , y , z are in A.P. , then the value of the determinant are in A....

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  12. Statement 1 is True: Statement 2 is True; Statement 2 is a correct ...

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  13. Comprehension 2 Consider the system of linear equations alphax+y...

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  14. Comprehension 2 Consider the system of linear equations alphax+y...

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  15. Without expanding the determinant prove that: |0b-c-b0a c-a0|=0

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  16. Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

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  17. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

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  18. By using properties of determinants. Show that:|1+a^2-b^2 2a b-2b2a b1...

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  19. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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  20. Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...

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