Home
Class 12
MATHS
Using the factor theorem it is found tha...

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant `|[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]|`. The other factor in the value of the determinant is

Text Solution

AI Generated Solution

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 factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a, a+b ,a+c],[ b+a,-2b,b+c],[c+a, c+b, -2c]|dot The other factor in the value of the determinant is (a) 4 (b) 2 (c) a+b+c (d) none of these

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

The value of the determinant |[a-b,b+c,a],[b-c,c+a,b],[c-a,a+b,c]| is

Without expanding the determinant, show that (a+b+c) is a factor of the determinant |[a, b, c], [b, c, a], [c, a, b]|

The value of the determinant |(b +c,a -b,a),(c +a,b -c,b),(a +b,c -a,c)| , is

Let a ,b ,c be positive and not all equal. Show that the value of the determinant |[a, b, c],[b, c, a],[ c, a ,b]| is negative.

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)

If a ne b ne c are all positive, then the value of the determinant |{:(a,b,c),(b,c,a),(c,a,b):}| is

Write the value of the following determinant |(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

    Text Solution

    |

  2. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

    Text Solution

    |

  3. Using the factor theorem it is found that a+b , b+c and c+a are thr...

    Text Solution

    |

  4. Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identi...

    Text Solution

    |

  5. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

    Text Solution

    |

  6. If Delta1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta2=|(1,b c, a),(1,c...

    Text Solution

    |

  7. The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n...

    Text Solution

    |

  8. Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,si...

    Text Solution

    |

  9. Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)|

    Text Solution

    |

  10. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

    Text Solution

    |

  11. Evaluate the determinant D=|[2 ,3,-2],[ 1, 2 ,3],[-2, 1,-3]| by expa...

    Text Solution

    |

  12. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]|

    Text Solution

    |

  13. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by method.

    Text Solution

    |

  14. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

    Text Solution

    |

  15. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

    Text Solution

    |

  16. If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

    Text Solution

    |

  17. If A=[1 2 4 2] , then show that |2A|=4|A| .

    Text Solution

    |

  18. If |[x-2 ,-3], [3x, 2x]|=3 , find the values of x

    Text Solution

    |

  19. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

    Text Solution

    |

  20. Evaluate the determinant =|((log)3 512,(log)4 3),((log)3 8,(log)4 9)...

    Text Solution

    |