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

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):}|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT PUBLICATION|Exercise ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(B))|97 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (4 MARK)|47 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANSWER TYPE QUESTIONS)|21 Videos

Similar Questions

Explore conceptually related problems

Show that without expanding at any stage |{:(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab):}|=0

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

Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=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))

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

Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Without expanding,show that the following determinant vanishes. abs((b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b^2,ab,a+b))

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

Without expanding,show that the following determinant vanishes. abs ((1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)))

ARIHANT PUBLICATION-DETERMINANTS -CHAPTER PRACTICE
  1. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

    Text Solution

    |

  2. Prove that: |[1, 1+p, 1+p+q],[2, 3+2p, 1+3p+2p], [3, 6+3p, 1+6p+3q ]|=...

    Text Solution

    |

  3. Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,c...

    Text Solution

    |

  4. IF a,b and c are in AP then find the value of the determinant |{:(x+2,...

    Text Solution

    |

  5. Without expanding evaluate the determinant , |{:(sina,sinbeta,sin(a+d...

    Text Solution

    |

  6. Prove that the determinant |{:(x, sin theta, cos theta),(-sin theta,...

    Text Solution

    |

  7. Using properties of determinants evaluate |{:(0,ab^2,ac^2),(a^2b,0,b...

    Text Solution

    |

  8. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

    Text Solution

    |

  9. Using properties of determinats show that |{:(a,a+b,a+2b),(a+2b,a,a+b)...

    Text Solution

    |

  10. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

    Text Solution

    |

  11. Evaluate |{:(1,1,1),(nC1,n+2C1,n+4C1),(nC2,n+2C2,n+4C2):}|

    Text Solution

    |

  12. Find the values of k, if the area of traingle is 4sq units and vertice...

    Text Solution

    |

  13. Show that the points A(a,b+c), B(b,c+a) and C(c,a+b) are collinear.

    Text Solution

    |

  14. IF A=[(1,3,3),(1,4,3),(1,3,4):}] then find |A|

    Text Solution

    |

  15. Find the inverse of the matrixA=[(a,b),(c,(1+bc)/a):}] and show that a...

    Text Solution

    |

  16. If A=[(2,2,1),(-2,1,2),(1,-2,2):}] and B=[(1,3,2),(1,1,1),(2,-3,1):}] ...

    Text Solution

    |

  17. If F(alpha)=[(cos a,-sina,0),(sina,cosa,0),(0,0,1):}]andG(beta)=[(cosb...

    Text Solution

    |

  18. Using matrices solve the following system of equations 4x+3y+2z=60,x+2...

    Text Solution

    |

  19. If A=[[1,-2,1],[0,-1,1],[2,0,-3]]then find A^(-1) and hence solve the ...

    Text Solution

    |

  20. If A=[(3,-4,2),(2,3,5),(1,0,1):}] then find A^-1 and hence solve the f...

    Text Solution

    |