Home
Class 12
MATHS
Prove the following: [[b^2-ab,b-c,bc-a...

Prove the following:
`[[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,c-a,ab-a^2]]=0`

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

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

Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+b^2]]=4a^2b^2c^2

Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+a^2+b^2+c^2

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2,ab]] = (a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]] =4ab

Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

Show that abs{:(b-c,c-a,a-b),(c-a,a-b,b-c),(a-b,b-c,c-a):}=0.

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

ARIHANT PUBLICATION-DETERMINANTS -CHAPTER PRACTICE
  1. Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. IFA=[(2,-1,1),(-1,2,-1),(1,-1,2):}]and B=[(3,1,-1),(1,3,1),(-1,1,3):}]...

    Text Solution

    |

  20. IF A=[(1,-2,0),(2,1,3),(0,-2,1):}]and B=[(7,2,-6),(-2,1,-3),(-4,2,5):}...

    Text Solution

    |