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Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2...

Prove that `|((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b+c)^3`

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

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

Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

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. Also find the value of the quotient.

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

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Without expanding, prove the following |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(a+b+c)(ab+bc+ca-a^2-b^2-c^2)

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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  2. Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^...

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  3. Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b...

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  4. If a, b, c are positive and unequal, show that value of the determinan...

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  5. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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  6. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

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  7. Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3.

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  8. Prove that : {:|(a^2a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b...

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  9. If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),...

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  10. Using determinant , find the area of triangle with verticles (1,0) ,...

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  11. Using determinants find the area of triangle with vertices (1,-1), ...

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  12. Find the area of the triangle with vertices at the points given in eac...

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  13. Find area of the triangle with vertices at the point given in the fol...

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  14. Find area of the triangle with vertices at the point given in the fol...

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  15. Using determinants, show that the following points are collinear: (1...

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  16. Using determinants, show that the following points are collinear: (-...

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  17. If the point (3,-2),(x,2),(8,8) are collinear, find 'x' using determin...

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  18. if area of triangle is 35sq.unit with vertices (2,-6) (5,4) and (K,4) ...

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  19. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  20. Determine the value of 'x' for which the area of the triangle formed b...

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