Home
Class 12
MATHS
Using properties of determinants prove t...

Using properties of determinants prove that
`|{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|=a^2 (a+x+y+z)`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    SHARAM PUBLICATION|Exercise EXAMPLE|156 Videos

  • DIFFERENTIAL EQUATION

    SHARAM PUBLICATION|Exercise EXAMPLE|124 Videos

Similar Questions

Explore conceptually related problems

Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3 or |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3

Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

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

Write the value of Delta=|{:(x+y,y+z,z+x),(z,x,y),(-3,-3,-3):}|

Using coafactors of the elements of third row, evaluate Delta=|{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Without expanding,show that the following determinant vanishes. abs((2x,x+y,x+z),(y+x,2y,y+z),(z+x,z+y,2z))

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

SHARAM PUBLICATION-DETERMINANT-EXAMPLE
  1. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

    Text Solution

    |

  2. Prove that |[x+y, x, x],[5x+4y, 4x, 2x], [10x+8y, 8x, 3x]|=x^3

    Text Solution

    |

  3. Using properties of determinants prove that |{:(a+x,y,z),(x,a+y,z),...

    Text Solution

    |

  4. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

    Text Solution

    |

  5. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

    Text Solution

    |

  6. Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(...

    Text Solution

    |

  7. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

    Text Solution

    |

  8. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

    Text Solution

    |

  9. Using the properties of determinants, show that abs[[1+a^2-b^2,2ab,-2b...

    Text Solution

    |

  10. Prove that: |[a, b, c],[a-b, b-c, c-a ], [b+c, c+a, a+b]|= a^3+b^3+c^3...

    Text Solution

    |

  11. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

    Text Solution

    |

  12. Using properties of the determinants, prove that: |[2y, y-z-x, 2y],[2z...

    Text Solution

    |

  13. Prove that: |[1, 1+p, 1+p+q],[2, 3+2p, 1+3p+2p], [3, 6+3p, 1+6p+3q ]|=...

    Text Solution

    |

  14. Show that: |[x, y ,z],[x^2, y^2, z^2], [yz, zx, xy ]|=(x-y)(y-z)(z-x)....

    Text Solution

    |

  15. Prove [[a^3-x^3,a^2,a],[b^3-x^3,b^2,b],[c^3-x^3,c^2,c]] = (a-b)(a-c)(b...

    Text Solution

    |

  16. Prove that: 1/(bc+ca+ab)|[a, b, c],[a^2, b^2, c^2], [bc, ca, ab]|=(b-c...

    Text Solution

    |

  17. Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

    Text Solution

    |

  18. Prove that: |[a+3b, a+5b, a+7b],[a+4b, a+6b, a+8b], [a+5b, a+7b, a+9b]...

    Text Solution

    |

  19. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

    Text Solution

    |

  20. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

    Text Solution

    |