Home
Class 12
MATHS
Prove that Det[[x+y+2z,x,y],[z,y+z+2x,y]...

Prove that `Det[[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]]=2(x+y+z)^3`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise NCERT FILE (Exercise 4.3)|9 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise NCERT FILE (Exercise 4.4)|7 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise NCERT FILE (Exercise 4.1)|13 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)

Using properties of determinants, prove that |[2y,y-z-x,2y],[2z,2z, z-x-y],[ x-y-z, 2x,2x]|=(x+y+z)^3

Prove that |[x+y, y+z, z+x] , [z+x, x+y, y+z] , [y+z, z+x, x+y]|=2|[x,y,z] , [z,x,y] , [y,z,x]|

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

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)

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

Prove that |[x,x^(2),x^(4)],[y,y^(2),y^(4)],[z,z^(2),z^(4)]|=xyz(x-y)(y-z)(z-x)(x+y+z)

prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

MODERN PUBLICATION-DETERMINANTS-NCERT FILE (Exercise 4.2)
  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. Using the property of determinants and without expanding, prove that:...

    Text Solution

    |

  5. Use the properties of determinant and without expanding prove that |...

    Text Solution

    |

  6. By using properties of determinants in |{:(0,a,-b),(-a,0,-c),(b,c,0):}...

    Text Solution

    |

  7. Using properties of determinants, prove that |-a^2a b a c b a-b^2b cc...

    Text Solution

    |

  8. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

    Text Solution

    |

  9. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

    Text Solution

    |

  10. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

    Text Solution

    |

  11. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

    Text Solution

    |

  12. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

    Text Solution

    |

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

    Text Solution

    |

  14. Prove that Det[[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]]=2(x+y+z)^3

    Text Solution

    |

  15. By using properties of determinants. Show that:|1xx^2x^2 1xxx^2 1|=(1-...

    Text Solution

    |

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

    Text Solution

    |

  17. Using properties of determinants, prove the following: |a^2a b a c...

    Text Solution

    |

  18. Let A be a square matrix of order 3xx3, then |k A|is equal to(A) k|A|...

    Text Solution

    |

  19. Which of the following is correct ?

    Text Solution

    |