Home
Class 12
MATHS
Using the property of determinants and w...

Using the property of determinants and without expanding prove that :
`{:|(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y)|=2|(a,p,x),(b,q,x),(c,r,z)|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • DIFFERENTIAL EQUATIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|507 Videos

Similar Questions

Explore conceptually related problems

Using the property of determinants and without expanding , prove that: |[b+c,q+r,y+z)],[c+a,r+p,z+x],[a+b,p+q,x+y]| = 2|[a,p,x],[b,q,y],[c,r,z]|

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

Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2|(a,b,c),(p,q,r),(x,y,z)|

Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x , y),(1,1,1):} = 0

Without expanding prove that |(a,b,c),(x,y,z),(p,q,r)| = |(y,b,q),(x,a,p),(z,c,r)|

Without expanding, prove the following |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

Without expanding , show that |(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|= 0 .

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Which of the following is correct

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |