Home
Class 12
MATHS
Evaluate Delta=|[1, a, bc],[ 1, b, c...

Evaluate `Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    V PUBLICATION|Exercise QUESTION BANK|168 Videos

  • DIFFERENTIAL EQUATIONS

    V PUBLICATION|Exercise QUESTION BANK|149 Videos

Similar Questions

Explore conceptually related problems

Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1, c, a+b]|

prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ba]| Without expanding, prove that Delta=0

Prove that |[1 , a , a^3],[ 1, b, b^3],[ 1, c, c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Evaluate |[1,1,1],[a,b,c],[b+c,c+a,a+b]|

|(1,a,b+c),(1,b,c+a),(1,c,a+b)| =

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

Without expanding the determinant prove the following. |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Prove that |[a, a+b, a+b+c],[ 2 a, 3 a+2 b, 4 a+3 b+2 c],[ 3 a, ...

    Text Solution

    |

  2. Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

    Text Solution

    |

  3. Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

    Text Solution

    |

  4. Using properties of determinants prove the following. abs[[b+c,a,...

    Text Solution

    |

  5. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

    Text Solution

    |

  6. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

    Text Solution

    |

  7. Without expanding the determinant prove the following. |[x,a,x+a],[y...

    Text Solution

    |

  8. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

    Text Solution

    |

  9. Evaluate |[2, 7, 65],[ 3, 8, 75],[ 5, 9, 86]|=0

    Text Solution

    |

  10. prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

    Text Solution

    |

  11. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

    Text Solution

    |

  12. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

    Text Solution

    |

  13. By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^...

    Text Solution

    |

  14. Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

    Text Solution

    |

  15. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

    Text Solution

    |

  16. Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

    Text Solution

    |

  17. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

    Text Solution

    |

  18. Using properties of determinants prove the following. abs[[1,x,x^2...

    Text Solution

    |

  19. Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b,...

    Text Solution

    |

  20. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

    Text Solution

    |