Home
Class 12
MATHS
prove that |(1/(a-a1)^2,1/(a-a1),1/a1),...

prove that `|(1/(a-a_1)^2,1/(a-a_1),1/a_1),(1/(a-a_2)^2,1/(a-a_2),1/a_2),(1/(a-a_3)^2,1/(a-a_3),1/a_3)|=(-a^2(a_1-a_2)(a_2-a_3)(a_3-a_1))/(a_1a_2a_3(a-a_1)^2(a-a_2)^2(a-a_3)^2)`.

Text Solution

Verified by Experts

The correct Answer is:
`-a^(2)(a_(1)-a_(2))(a_(2)-a_(3))(a_(3)-a_(1))`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

If (a_2a_3)/(a_1a_4) = (a_2+a_3)/(a_1+a_4)=3 ((a_2 -a_3)/(a_1-a_4)) then a_1,a_2, a_3 , a_4 are in :

Prove that ((a_1)/(a_2)+(a_3)/(a_4)+(a_5)/(a_6)) ((a_2)/(a_1)+(a_4)/(a_3)+(a_6)/(a_5)) geq 9

If (a_2 a_3)/(a_1 a_4) = (a_2 + a_3)/(a_1 + a_4) = 3 ((a_2 - a_3)/(a_1 - a_4)) then a_1, a_2, a_3, a_4 are in

Find the coefficient of x in the determinant |((1+x)^(a_1 b_1),(1+x)^(a_1 b_2),(1+x)^(a_1 b_3)),((1+x)^(a_2 b_2),(1+x)^(a_2 b_2),(1+x)^(a_2 b_3)),((1+x)^(a_3 b_3),(1+x)^(a_3 b_2),(1+x)^(a_3 b_3))|=0.

If a_1,a_2,a_3,………….a_12 are in A.P. and /_\_1 =|(a_1a_5, a_1,a_2),(a_2a_6,a_2,a_3),(a_3a_7,a_3,a_4)|, |(a_2a_10, a_2,a_3),(a_3a_11,a_3,a_4),(a_4_12,a_4,a_5)| then /_\_1:/_\_2= (A) 1:2 (B) 2:1 (C) 1:1 (D) none of these

If the nonzero numbers a_1,a_2,a_3,....,a_n are in AP, prove that 1/(a_1a_2a_3)+1/(a_2a_3a_4)+...+1/(a_(n-2)a_(n-1)a_n)=1/(2(a_2-a_1))(1/(a_1a_2)-1/(a_(n-1)a_n)) .

If a_1,a_2,….a_n are in H.P then (a_1)/(a_2+,a_3,…,a_n),(a_2)/(a_1+a_3+….+a_n),…,(a_n)/(a_1+a_2+….+a_(n-1)) are in

The determinant |(b_1+c_1,c_1+a_1,a_1+b_1),(b_2+c_2,c_2+a_2,a_2+b_2),(b_3+c_3,c_3+a_3,a_3+b_3)|=

ARIHANT MATHS-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,c,b),(c,c+a,a),(b,a,a+b):}| =4 abc.

    Text Solution

    |

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

    Text Solution

    |

  3. Find the value of determinat |{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(...

    Text Solution

    |

  4. The value of the determinant |(bc,ca,ab),(p,q,r),(1,1,1)|, where a, b ...

    Text Solution

    |

  5. Whitout expanding the determinat at any stage prove that |{:(-5,3+5i,...

    Text Solution

    |

  6. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

    Text Solution

    |

  7. If A,B and C are the angles of a triangle and |{:(1,1,1),(1+sinA,1+si...

    Text Solution

    |

  8. The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...

    Text Solution

    |

  9. If y=(u)/(v), where u and v are functions of x, show that v^(3)(d^(2...

    Text Solution

    |

  10. Show that the determinant Delta (x) is given by Delta(x) = |{:(sin(...

    Text Solution

    |

  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

    Text Solution

    |

  13. If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...

    Text Solution

    |

  14. prove that |(1/(a-a1)^2,1/(a-a1),1/a1),(1/(a-a2)^2,1/(a-a2),1/a2),(1/...

    Text Solution

    |

  15. Show that in general there are three values of t for which the followi...

    Text Solution

    |

  16. Eliminates (i) a,b, and c (ii) x,y,z from the equations -a+(by)...

    Text Solution

    |

  17. If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...

    Text Solution

    |