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Prove that: {:|(1+a^2-b^2,2ab,-2b),(2a...

Prove that:
`{:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-b^2)|`

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Without expanding, prove the following |(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+6^2,2a),(2a,-2a,1-a^2-b^2)|=(1+a^2+b^2 )^3

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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  2. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  3. Prove that: {:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-...

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  4. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  5. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  6. Which of the following is correct

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

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

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

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  10. Show that points : A (a,b+c),B(b,c+a),C(c,a+b) are collinear.

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  11. Find the value of k if the area of the triangle is 4 sq. units whose v...

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

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

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

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  15. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

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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. Write Minors and Cofactors of the elements of following determinant : ...

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  19. Write Minors and Cofactors of the elements of following determinant : ...

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  20. Using Cofactors of elements of second row, evaluate triangle = |[5,3,8...

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