Home
Class 12
MATHS
Without expanding show that following : ...

Without expanding show that following : `|[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]| = a^3`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Prove that |(a,a+b, a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a,6b+3c)| = a^3

Expand the following (3a-2b)^3

Without expanding the following determinant, show that : |[3a+b, 2a, a],[4a+3b, 3a, 3a],[5a+6b,4a,6a]|=a^3

Without expanding, prove the following |(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2b,b^2c,0)|=2a^3b^3c^3

Without expanding, prove the following |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^3+b^3+c^3-3abc

Expand the following (3a-5b-c)^2

Without expanding show that the following determinants vanish |(4,a,b+c),(4,b,c+a),(4,c,a+b)|

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]|

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

    Text Solution

    |

  2. Find the inverse of the matrix A = {:[(a,b),(c,(1+bc)/a)] and show tha...

    Text Solution

    |

  3. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

    Text Solution

    |

  4. If A = [[2,-3,5],[3,2,-4],[1,1,-2]] find A^-1. Using A^-1 solve the s...

    Text Solution

    |

  5. Let P = [[3, -1, -2],[2 ,0 ,alpha ],[3, -5, 0]], where alpha in R. Sup...

    Text Solution

    |

  6. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

    Text Solution

    |

  7. Let M and n be two 3xx3 matrices such that MN = NM. Further, If Mne ...

    Text Solution

    |

  8. For 3xx3 martrices M and N, which of the following statement (s) is ...

    Text Solution

    |

  9. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

    Text Solution

    |

  10. If A is a matrix of order mxx m such that A^(2) +A + 2I = O, then

    Text Solution

    |

  11. Let a, b, and c be three real numbers satisfying [(a,b,c)][[1,9,7],[...

    Text Solution

    |

  12. Let omega be a solution of z^3-1 = 0 If a = 2 , b=8 and c =7 then the ...

    Text Solution

    |

  13. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  14. A complex number U = 4+2i.The value of |U| is

    Text Solution

    |

  15. Let A be the set of all 3× 3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  16. Let A be the set of all 3xx3 symmetric matrices all of whoes entries...

    Text Solution

    |

  17. For a 2xx2 matrix, A = [a(ij)], whose elements are given by a(ij) = ...

    Text Solution

    |

  18. If A is a square matrix such that A^2 = A, then write the value of (I+...

    Text Solution

    |

  19. Evaluate the following determinants: {:|(3,x),(x,1)| = |(3,2),(4,1)|

    Text Solution

    |

  20. If Delta={:|(1,2,3),(2,0,1),(5,3,8)|, write the minor of the element a...

    Text Solution

    |