Home
Class 12
MATHS
Without expanding the determinant prove...

Without expanding the determinant prove the following.
`|[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=0`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    A N EXCEL PUBLICATION|Exercise QUESTION TYPE|83 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |158 Videos

  • DIFFERENTIAL EQUATIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |134 Videos

Similar Questions

Explore conceptually related problems

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

Without expanding the determinant prove the following. |[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

Without expanding the determinant prove the following. |[b+c,q+r,y+z],[c+a,r+p,z+x],[a+b,p+q,x+y]|=2|[a,p,x],[b,q,y],[c,r,z]|

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

Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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]|

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

Using properties of determinants prove the following. abs[[1,1,1],[a,b,c],[a^3,b^3,c^3]]=(a-b)(b-c)(c-a)(a+b+c)

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

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

    Text Solution

    |

  2. Without expanding the determinant prove the following. |[1,bc,a(b+c)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

    Text Solution

    |

  7. Using properties of determinants prove the following. abs[[1,1,1],...

    Text Solution

    |

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

    Text Solution

    |

  9. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

    Text Solution

    |

  10. By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],...

    Text Solution

    |

  11. Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-...

    Text Solution

    |

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

    Text Solution

    |

  16. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

    Text Solution

    |

  17. Which of the following is correct?

    Text Solution

    |

  18. Consider a triangle whose vertices are (3,8),(-4,2) and (5,1) Find are...

    Text Solution

    |

  19. Find the equation of the line joining A(1,3) and B(0,0) using determin...

    Text Solution

    |

  20. Find the adjoint of A= [(1,2),(3,4)]

    Text Solution

    |