Home
Class 12
MATHS
Prove that: |-2a a+b a+c b+a-2bb+cc+a c+...

Prove that: `|-2a a+b a+c b+a-2bb+cc+a c+b-2c|=4(a+b)(b+c)(c+a)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Expansion of Determinant|5 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Single Option Correct Type Questions|10 Videos

  • DEFINITE INTEGRAL

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

  • DIFFERENTIAL EQUATION

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

Similar Questions

Explore conceptually related problems

Using the property of determinants and without expanding, prove that: |-a^2a b a c b a b^2b cc a c b-c^2|=4a^2b^2c^2

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

Using the property of determinants and without expanding, prove that: |[-a^2,a b, a c],[ b a, -b^2,b c],[c a, c b,-c^2]|=4a^2b^2c^2

Prove that: |(-2a , a+b, a+c),( b+a,-2b, b+c),( c+a , c+b,-2c)|=4(a+b)(b+c)(c+a)

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c^2 .

Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=(a-b)^2+(b-c)^2+(c-a)^2

Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that: |-2a a+b a+c b+a-2bb+cc+a c+b-2c|=4(a+b)(b+c)(c+a)

    Text Solution

    |

  2. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

    Text Solution

    |

  3. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  4. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k for which the linear equations 4x+ky+2...

    Text Solution

    |

  11. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  12. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  13. if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

    Text Solution

    |

  14. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

    Text Solution

    |

  17. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  18. Let alpha, lambda , mu in R.Consider the system of linear equations ...

    Text Solution

    |

  19. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |