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Using the properties of determinants, pr...

Using the properties of determinants, prove the following
`|{:((a+b)^2,ca,cb),(ca,(b+c)^2,ab),(bc,ab,(c+a)^2):}|=2abc(a+b+c)^3`

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The correct Answer is:
`2abc(a+b+c)^3`
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Using the property of determinants and without expanding prove the following |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Using the properties of determinants, prove the following It 2s=a+b+c then |{:(a^2,(s-a)^2,(s-a)^2),((s-b)^2,b^2,(s-b)^2),((s-c)^2,(s-c)^2,c^2):}|=2s^3(s-a)(s-b)(s-c)

Using the property of determinants and without expanding prove the following |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

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KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. If a,b,c are A.P then |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}...

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

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  3. Using the properties of determinants, prove the following |{:((a+b)^...

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  4. Find area of the triangle withh vertices at the point given in each of...

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  5. Find area of the triangle withh vertices at the point given in each of...

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  6. Find area of the triangle withh vertices at the point given in each of...

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  7. Find area of the triangle with vertices at the point given in each of ...

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  8. Find values of k if area of triangle is 4 sq. units and vertices are (...

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  9. Find values of k if the points (3,5), (k,3) and (1,1) are collinear

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  10. Find values of k if area of trianlge is 13 and vertices are (8,2), (k,...

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  11. Find the equation of line passing through the given points using deter...

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  12. Find the equation of line passing through the given points using deter...

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  13. Find the equation of line passing through the given points using deter...

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  14. Find the equation of line passing through the given points using deter...

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  15. Write minors and cofactors of the elements of following determinant ...

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  16. Write minors and cofactors of the elements of following determinant ...

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  17. Write minors and cofactors of the elements of following determinant ...

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  18. Verify: The value of the determinant remains unchanged if its rows and...

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  19. Write minors and cofactors of the elements of following determinant ...

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  20. Uing cofactors of elements of first row evaluate |{:(2,-1,3),(6,4,16),...

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