Home
Class 12
MATHS
Solve the system of equations : z+ay+a^2...

Solve the system of equations : `z+ay+a^2x+a^3=0 z+by+b^2x+b^3=0 z+cy+c^2x+c^3=0]` where `a != b != c.`

Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    ALLEN|Exercise EX -JA|8 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    ALLEN|Exercise All Questions|145 Videos

Similar Questions

Explore conceptually related problems

Solve the system of equations : z+ay+a^(2)x+a^(3)=0z+by+b^(2)x+b^(3)=0z+cy+c^(2)x+c^(3)=0] where a!=b!=c

Solve the system of equations 2x+3y-3z=0 , 3x-3y+z=0 and 3x-2y-3z=0

If the system of linear equation x + 4ay + ax = 0 , x + 3b + bz = 0 x + 2cy + cz = 0 have a non-trivial solution, then a, b, c are in

If the system of linear equations 2x + 2y +3z =a 3x - y +5z =b x- 3y +2z =c where a, b, c are non-zero real numbers, has more than one solution, then

Consider the system of equation x+2y-3z=a , 2x+6y-11z=b , x-2y+7c then

Solve the following system of homogeneous equations: 2x+3y-z=0x-y-2z=03x+y+3z=0

The solution of the system of equations a^(2)x+ay+z=-a^(3),b^(2)x+by+z=-b^3, c^2x+cy +z=-c^(3) is (A) x=-(a+b+c),y=ab+bc+ca,z=-abc (B) x=(a+b+c),y=ab+bc+ca,z=-abc (C) x=-(a-b-c),y=ab+bc+ca,z=-abc (D) None of these

If the system of equations ax + by + c = 0,bx + cy +a = 0, cx + ay + b = 0 has infinitely many solutions then the system of equations (b + c) x +(c + a)y + (a + b) z = 0(c + a) x + (a+b) y + (b + c) z = 0(a + b) x + (b + c) y +(c + a) z = 0 has

Solve the following system of homogenous linear equations : 2x+3y+4z=0 , x+y+z=0 , 2x-y+3z=0

ALLEN-DETERMINANTS-All Questions
  1. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

    Text Solution

    |

  2. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

    Text Solution

    |

  3. Solve the system of equations : z+ay+a^2x+a^3=0 z+by+b^2x+b^3=0 z+cy+c...

    Text Solution

    |

  4. If x ,\ y , z are not all zero and if a x+b y+c z=0; b x+c y+a z=0; c ...

    Text Solution

    |

  5. If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1...

    Text Solution

    |

  6. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  7. If D=|1 1 1 1 1+x1 1 1 1+y|"f o r"x!=0, y!=0 then D is (1) divisibl...

    Text Solution

    |

  8. Let a, b, c be any real numbers. Suppose that there are real number...

    Text Solution

    |

  9. Let a, b, c be such that b(a""+""c)!=0 . If |a a+1a-1-bb+1b-1cc-1c...

    Text Solution

    |

  10. Consider the system of linear equations; x-1\ +2x2+x3=3 2x1+3x2+3=3 3x...

    Text Solution

    |

  11. The number of value of k for which the linear equations 4x+k y+2z=0k x...

    Text Solution

    |

  12. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  13. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  14. If a ,b ,c are sides of a scalene triangle, then value of |a b c b c a...

    Text Solution

    |

  15. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

    Text Solution

    |

  16. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

    Text Solution

    |

  17. Consider the system of equations x+a y=0,\ y+a z=0.\ Then the set of ...

    Text Solution

    |

  18. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

    Text Solution

    |

  19. The set of all values of lamda for which the system of linear equation...

    Text Solution

    |

  20. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

    Text Solution

    |