Home
Class 12
MATHS
By using properties of determinants, sh...

By using properties of determinants, show that : `|[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • DIFFERENTIAL EQUATIONS

    PSEB|Exercise Exercise|116 Videos

Similar Questions

Explore conceptually related problems

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

Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y+z,y^2+z^2],[1,z+x,z^2+x^2]| = (x-y)(y-z)(z-x)

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .

Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

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

Using properties of determinants, prove that : {:|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y),(1,1,1)|

Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z)(z+x)

PSEB-DETERMINANTS-Exercise
  1. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Which of the following is correct

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If area of triangle is 4 sq. units with vertices (-2, 0), (0, 4) and (...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |