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Using the property of determinants and w...

Using the property of determinants and without expanding , prove that: `|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b]| = 0`

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Using the property of determinants and without expanding , prove that: |[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]| = 0

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Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Using the properties of determinants, prove that : |[[x+a,b,c],[a,x+b,c],[a,b,x+c]]| = x^2(x+a+b+c)

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

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

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  2. Using the property of determinants and without expanding , prove that:...

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  3. Using the property of determinants and without expanding , prove that:...

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  4. Using the property of determinants and without expanding prove that : ...

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

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

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

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

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

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

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

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

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

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

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  18. Which of the following is correct

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

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

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