Home
Class 12
MATHS
Without expanding, prove the following ...

Without expanding, prove the following
`|(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION IV) |7 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION V) |21 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION II) (SHORT ANSWER TYPE QUESTIONS )|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)|94 Videos

  • DIFFERENTIAL EQUATIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE|50 Videos

Similar Questions

Explore conceptually related problems

Without expanding, prove the following |(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=xyz(x-y)(y-z)(z-x)

Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x , y),(1,1,1):} = 0

Without expanding prove that |(a,b,c),(x,y,z),(p,q,r)| = |(y,b,q),(x,a,p),(z,c,r)|

Using properties of determinants, prove that : {:|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

Without actual expansion, prove that the following determinants vanish: {:|(x,a,x+a),(y,b,y+b),(z,c,z+c)|

Without expanding , show that |(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|= 0 .

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION III)
  1. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

    Text Solution

    |

  2. Without expanding, prove the following |(0,ab^2,ac^2),(a^2b,0,bc^2)...

    Text Solution

    |

  3. Without expanding, prove the following |(y+z,z,y),(z,z+x,x),(y,x,x+...

    Text Solution

    |

  4. Without expanding, prove the following |(a,a+b,a+2b),(a+2b,a,a+b),(...

    Text Solution

    |

  5. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

    Text Solution

    |

  6. Without expanding, prove the following |(1+a^2-b^2,2ab,-2b),(2ab,1-...

    Text Solution

    |

  7. Without expanding, prove the following |(x,x+y,x+2y),(x+2y,x,x+y),(...

    Text Solution

    |

  8. Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

    Text Solution

    |

  9. Without expanding, prove the following |(1,a,a^3),(1,b,b^3),(1,c,c^...

    Text Solution

    |

  10. Without expanding, prove the following |(x,y,z),(x^2,y^2,z^2),(x^3,...

    Text Solution

    |

  11. Without expanding, prove the following |(1,1,1),(alpha,beta,gamma),...

    Text Solution

    |

  12. Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,c...

    Text Solution

    |

  13. Without expanding, prove the following |(a^3+1,a^2,a),(b^3+1,b^2,b)...

    Text Solution

    |

  14. Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q)...

    Text Solution

    |

  15. Without expanding, prove the following |(b+c,c+a,a+b),(c+a,a+b,b+c)...

    Text Solution

    |

  16. Without expanding, prove the following |(a^2,2ab,b^2),(b^2,a^2,2ab)...

    Text Solution

    |

  17. Without expanding, prove the following |(a,b-c,c-b),(a-c,b,c-a),(a-...

    Text Solution

    |

  18. Without expanding, prove the following |(a,b,c),(a-b,b-c,c-a),(b+c,...

    Text Solution

    |

  19. Solve the equation |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0

    Text Solution

    |

  20. Solve the equation |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)...

    Text Solution

    |