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If a, b, c are positive and unequal, sho...

If a, b, c are positive and unequal, show that value of the determinant `triangle = |[a,b,c],[b,c,a],[c,a,b]|` is negative.

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^...

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

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

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

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

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  7. 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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  8. 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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  9. Using determinant , find the area of triangle with verticles (1,0) ,...

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

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

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

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

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

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

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

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

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

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

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  20. Find equation of line joining (1, 2) and (3, 6) using determinants.

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