Home
Class 12
MATHS
Show that |[1,b c, a(b+c)],[1,c a, b(c+a...

Show that `|[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0` .

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 property of determinants and without expanding, prove that: |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0

Show that |[1,a ,b+c],[1,b, c+a],[1,c ,a+b]|=0 .

Using the property of determinants and without expanding, prove that: |1b c a(b+c)1c a b(c+a)1a b x(a+b)|=0

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

Show that |1a b_c1b c+a1c a+b|=0

Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a b+b c+c a) .

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Show that |[1,a ,b+c],[1,b, c+a],[1,c ,a+b]|=0 .

    Text Solution

    |

  2. Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

    Text Solution

    |

  3. Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

    Text Solution

    |

  4. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

    Text Solution

    |

  5. Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2th...

    Text Solution

    |

  6. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

    Text Solution

    |

  7. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

    Text Solution

    |

  8. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

    Text Solution

    |

  9. Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1...

    Text Solution

    |

  10. If a ,\ b ,\ c are in A.P., find the value of |(2y+4, 5y+7, 8y+a),(3...

    Text Solution

    |

  11. Without expanding evaluate the determinant =|(265, 240, 219), (240, ...

    Text Solution

    |

  12. If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , with...

    Text Solution

    |

  13. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

    Text Solution

    |

  14. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

    Text Solution

    |

  15. If A is a skew-symmetric matrix of odd order n , then |A|=O .

    Text Solution

    |

  16. Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

    Text Solution

    |

  17. Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b)...

    Text Solution

    |

  18. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

    Text Solution

    |

  19. Prove that: |-a^2 ab ac ba -b^2 bc ...

    Text Solution

    |

  20. Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

    Text Solution

    |