Home
Class 12
MATHS
If 1=|1 1 1x^2y^2z^2x y z| and 2=|1 1 1y...

If `_1=|1 1 1x^2y^2z^2x y z|` and `_2=|1 1 1y z z xx y x y z|` , without expanding prove that `_1=_2` .

Text Solution

Verified by Experts

145829
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos
  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

If _1=|1 1 1x^2y^2z^2x y z|a n d_2=|1 1 1y z z xx y x y z|, without expanding prove that _1=_2

If Delta_1 = |[1,1,1] , [x^2, y^2, z^2] , [x,y,z]| and Delta_2=|[1,1,1] , [yz, zx, xy] , [x,y,z]| then without expanding show that Delta_1= Delta_2

Without expanding prove that det[[x+y,z,1y+z,x,1z+x,y,1]]=0

8x + y + 2z = 4x + 2y + z = 1x + y + z = 2

If cos^-1 x+cos^-1 y+cos^-1 z=pi and x+y+z= 3/2, then prove that x=y=z

If |[x^3+1, x^2, x] , [y^3+1, y^2, y] , [z^3+1, z^2, z]|=0 and x, y, z are all different then prove that xyz=-1

If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y and z are not equal to any other, prove that, xyz = -1

2x-3z + w = 1x-y + 2w = 1-3y + z + w = 1x + y + z = 1

Without expanding,prove that quad Delta=det[[x+y,y+z,z+xz,x,y1,1,1]]=0

If a = 2 , x = 1, y = 1 , z = 1 then find the value of a^x times a^y times a^z

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If a ,\ b ,\ c are in A.P., find the value of |2y+4 5y+7 8y+a3y+5 6...

    Text Solution

    |

  2. Without expanding evaluate the determinant =|265 240 219 240 225 19...

    Text Solution

    |

  3. If 1=|1 1 1x^2y^2z^2x y z| and 2=|1 1 1y z z xx y x y z| , without exp...

    Text Solution

    |

  4. Let =|A xx^2 1B y y^2 1C z z^2 1| and 1=|A B C x y z y z z xx y| , the...

    Text Solution

    |

  5. If 1=|a b c x y z p q r| and 2=|q-b y-p a-x r-c z| , without expanding...

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that: |0a-b-a0-c b c0|=0 .

    Text Solution

    |

  8. Without expanding or evaluating show that |0b-a c-a a-b0c-b a-c b-c...

    Text Solution

    |

  9. Without expanding, prove that |a+b x c+dx p+q x a x+b c x+d p x+q u...

    Text Solution

    |

  10. Prove that: |-a^2a b a c b a-b^2b c a c b c-c^2|=4a^2b^2c^2 .

    Text Solution

    |

  11. Prove that: |1 1 1 1 1+x1 1 1 1+y|=x y .

    Text Solution

    |

  12. Evaluate: |1a a^2 1bb^2 1cc^2| .

    Text Solution

    |

  13. Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

    Text Solution

    |

  14. Prove that: |alphabetagammaalpha^2beta^2gamma^2beta+gammagamma+alphaal...

    Text Solution

    |

  15. In a triangleABC, if |[1,1,1][1+sinA,1+sinB,1+sinC],[sinA+sin^2A,sinB+...

    Text Solution

    |

  16. In a A B C ,if|1 1 1 1+cosA1+cosB1+cosCcos^2A+cosBcos^2A+cosBcos^2+co...

    Text Solution

    |

  17. Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,...

    Text Solution

    |

  18. If x!=y!=z and |xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0 , then prove that ...

    Text Solution

    |

  19. For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...

    Text Solution

    |

  20. Using properties of determinants, show that |1a a^2-b c1bb^2-c a1cc...

    Text Solution

    |