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Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],...

Prove that: `|[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Using the property of determinants and without expanding prove that : ...

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  2. By using properties of determinants, Show that : {:|(0,a,-b),(-a,0,-...

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  3. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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

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  5. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

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  6. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

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  7. Prove that: |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2.

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

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

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

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

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

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  15. Which of the following is correct

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

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

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

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

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

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