Home
Class 12
MATHS
Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a...

Prove that : `|{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(3)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4c|7 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4d|13 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4a|6 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

Similar Questions

Explore conceptually related problems

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

Prove that |(a+b, b, c), (b+c, c, a), (c+a, a, b)| = 3abc - a^3-b^3-c^3.

[[ Prove that ,,a+b,b,cb+c,c,ac+a,a,b]]=3abc-a^(3)-b^(3)-c^(3)

[[b+c,a-b,ac+a,b-c,ba+b,c-a,c]]=3abc-a^(3)-b^(3)-c^(3)

Prove that |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=- 2 (a^3+ b^3+c^3-3abc)

|(1,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^(3)+b^(3)+c^(3)-3ab

|(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

Let a,b,c in R be such that a+b+c gt 0 and abc = 2 . Let A = [(a,b,c),(b,c,a),(c,a,b)] If A^(2)=I then value of a^(3)+b^(3)+c^(3) is

det[[a,b,ca-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc

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

NAGEEN PRAKASHAN-DETERMINANTS-Exercise 4b
  1. Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}|

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

    Text Solution

    |

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

    Text Solution

    |

  6. Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2)...

    Text Solution

    |

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

    Text Solution

    |

  8. Prove that : |{:(a^(2),b^(2)+c^(2),bc),(b^(2),c^(2)+a^(2),ca),(c^(2),a...

    Text Solution

    |

  9. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

  10. Find the value of |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|

    Text Solution

    |

  11. Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0

    Text Solution

    |

  12. Find the value of x |[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]|=0

    Text Solution

    |

  13. (i) Solve the equation |{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-...

    Text Solution

    |

  14. Solve the equation |{:(x+a,c+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0

    Text Solution

    |

  15. One root of the equation |(3x-8, 3, 3),(3,3x-8, 3),(3,3,3x-8)|=0 si (A...

    Text Solution

    |

  16. If 2 s=a+b+c, then show that : |{:(a^(2),(s-a)^(2),(s-a)^(2)),((s-b)^(...

    Text Solution

    |

  17. If the sides of a DeltaABC and a, b, c and |{:(a^(2),b^(2),c^(2)),((a+...

    Text Solution

    |

  18. If the pth, qth and rth terms of a G.P, are x,y and z repectively, the...

    Text Solution

    |

  19. Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(x+y+...

    Text Solution

    |

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

    Text Solution

    |