Home
Class 12
MATHS
Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],...

Show that: `|[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • DIFFERENTIAL EQUATIONS

    PSEB|Exercise Exercise|116 Videos

Similar Questions

Explore conceptually related problems

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

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

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^2, (c+a)^2, b^2],[c^2,c^2,(a+b)^2]]|= 2abc (a+b+c)^3 .

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

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

PSEB-DETERMINANTS-Exercise
  1. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

    Text Solution

    |

  2. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

    Text Solution

    |

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

    Text Solution

    |

  4. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

    Text Solution

    |

  5. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

    Text Solution

    |

  6. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

    Text Solution

    |

  7. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

    Text Solution

    |

  8. Which of the following is correct

    Text Solution

    |

  9. Find area of the triangle with vertices at the point given in the fol...

    Text Solution

    |

  10. Find area of the triangle with vertices at the point given in the fol...

    Text Solution

    |

  11. Find area of the triangle with vertices at the point given in the fol...

    Text Solution

    |

  12. Show that points A(a,b+c),B(b,c+a) ਅਤੇ C(c,a+b) are collinear.

    Text Solution

    |

  13. Find the value of k if the area of the triangle is 4 sq. units whose v...

    Text Solution

    |

  14. If area of triangle is 4 sq. units with vertices (-2, 0), (0, 4) and (...

    Text Solution

    |

  15. Find equation of line joining (1, 2) and (3, 6) using determinants.

    Text Solution

    |

  16. Find equation of line joining (3, 1) and (9, 3) using determinants.

    Text Solution

    |

  17. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

    Text Solution

    |

  18. Write Minors and Cofactors of the elements of following determinant : ...

    Text Solution

    |

  19. Write Minors and Cofactors of the elements of following determinant : ...

    Text Solution

    |

  20. Write Minors and Cofactors of the elements of following determinant : ...

    Text Solution

    |