Home
Class 12
MATHS
Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1...

Prove that `|{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(abc+bc+ca+ab)`

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 6

    MODERN PUBLICATION|Exercise EXERCISE|43 Videos

  • TEST PAPER 8

    MODERN PUBLICATION|Exercise EXERCISE|40 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)

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

Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/a+/b+1/c)

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

Without expanding the determinants 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):}|

Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Without expanding prove abs((bc, a, a^2),(ca, b, b^2),(ab, c, c^2))=abs((1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3))

Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

MODERN PUBLICATION-TEST PAPER 7-EXERCISE
  1. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  2. An animal feed company must produce 200kg of a mixture consisting of i...

    Text Solution

    |

  3. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

    Text Solution

    |

  4. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

    Text Solution

    |

  5. Express as a sum of a symmetric and a skew symmetric matrix: [[x,a,b],...

    Text Solution

    |

  6. Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,c...

    Text Solution

    |

  7. Test differentiability of the following function at the indicated poin...

    Text Solution

    |

  8. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

    Text Solution

    |

  9. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

    Text Solution

    |

  10. If tangents are drawn from the origin to the curve y = sin x then sho...

    Text Solution

    |

  11. Test the function y = (x - 5)^5( x + 2)^2 for extreme values.

    Text Solution

    |

  12. Evaluate : int ((sinxcosx)/(sin2x) - 2sinx+3)dx .

    Text Solution

    |

  13. int0^(pi/2)(cosxdx)/((sinx+1)(sinx+2))

    Text Solution

    |

  14. Solve : (x + 2y^3)dy/dx = y.

    Text Solution

    |

  15. Find the general solution of dy/(du) = u+1/sqrtu + 6u + 5.

    Text Solution

    |

  16. Prove the following by vector method. The diagonals of a rhombus are a...

    Text Solution

    |

  17. Find the equation of the plane passing through the line of intersectio...

    Text Solution

    |

  18. Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...

    Text Solution

    |

  19. Obtain the equation of the line through the point (1, 2, 3) and parall...

    Text Solution

    |

  20. Find the inverse of the following matrices using elementary transforma...

    Text Solution

    |