Home
Class 12
MATHS
Prove that: |(-2a , a+b, a+c),( b+a,-2b...

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

Text Solution

AI Generated Solution

To prove that \[ \begin{vmatrix} -2a & a+b & a+c \\ b+a & -2b & b+c \\ c+a & c+b & -2c \end{vmatrix} ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

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

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

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

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

Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2) .

Prove that |{:(b+c, c+a, a+b),(c+a, a+b,b+c),(a+b, b+c, c+a):}| =2(a+b+c)(ab+bc+ca-a^(2)-b^(2)-c^(2)).

Prove that |{:(a,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)

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

Prove that : |{:(x+a,b,c),(a,x+b,c),(a,b,x+c):}|=x^(2)(x+a+b+c)

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

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b,...

    Text Solution

    |

  2. Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x...

    Text Solution

    |

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

    Text Solution

    |

  4. Evaluate the following determinant: |[1 ,3, 5], [2 ,6, 10], [31, 11,...

    Text Solution

    |

  5. Evaluate the following determinant: |[1, 4, 9], [4 ,9 ,16], [9, 16, ...

    Text Solution

    |

  6. Without expanding, show that the value of each of the following dete...

    Text Solution

    |

  7. Without expanding, show that the value of each of the following dete...

    Text Solution

    |

  8. Without expanding, show that the value of the following determinant ...

    Text Solution

    |

  9. Without expanding, show that the value of each of the following det...

    Text Solution

    |

  10. Without expanding, show that the value of the following determinant...

    Text Solution

    |

  11. Without expanding, show that the value of each of the following dete...

    Text Solution

    |

  12. Evaluate the following: |[1,a, b c],[1,b, c a],[1,c, a b]|

    Text Solution

    |

  13. Evaluate the following: |[0,x y^2,x z^2],[x^2y,0,y z^2],[x^2z, z y^2,...

    Text Solution

    |

  14. If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"1=|(1, 1, 1),(...

    Text Solution

    |

  15. Prove:\ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

    Text Solution

    |

  16. Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^...

    Text Solution

    |

  17. Prove: |(a+b,b+c,c+a),( b+c,c+a, a+b),( c+a, a+b,b+c)|=2|(a, b, c),( b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-...

    Text Solution

    |