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Prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b...

Prove that `|{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^(3)`.

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Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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Prove that: |{:(-2a, a+b, a+c), (b+a,-2b,b+c),(c+a, c+b,-2c):}|=4(a+b)(b+c)(c+a)

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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)

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2.

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  2. using properties of determinant, prove that abs{:(y+k , y , y ),(y , y...

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  3. Prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^(3)...

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  4. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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

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

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

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  9. Which of the following is correct

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

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

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

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

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

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

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

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

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

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

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