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Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10...

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

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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

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  4. 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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  5. 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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  6. Using determinant , find the area of triangle with verticles (1,0) ,...

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

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

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

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

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

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

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

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

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

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

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

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  18. Find equation of line joining (3, 1) and (9, 3) using determinants.

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  19. Find the equation of the line joining A(1, 3) and B (0, 0) using deter...

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  20. Prove that area of the trianlge whose vertices are (at1^2,2at1) , (at2...

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