Home
Class 12
MATHS
If a , b , c are distinct real numbers a...

If `a , b , c` are distinct real numbers and the system of equations `a x+a^2y+(a^3+1)z=0` `b x+b^2y+(b^3+1)z=0` `c x+c^2y+(c^3+1)=0` has a non-trivial solution, show that `a b c=-1`

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

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y=z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y+z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then ab+bc+ca equals to (A) abc (B) a^2 - b^2 + c^2 (C) a+b -c (D) None of these

The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z = 0 has non-trivial solution if a, b, c are in

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

If a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to

Prove that the system of equations in xa +y+z=0 , x +by +z=0 , x +y+cz=0 has a non - trivial solution then 1/(1-a) + 1/(1-b)+ 1/(1-c)=

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0, alphax+(alpha+b)y+alphaz=0, alphax+alphay+(alpha+c)z=0 has a non-trivial solution if

If the system of equations x=c y+b z y=a z+c x z=b x+a y has a non-trivial solution, show that a^2+b^2+c^2+2a b c=1

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 , a x+(q+b)y+c z=0 , a x+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is a. -1 b. 0 c. 1 d. 2

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Find the value of lambda for which the homogeneous system of equations...

    Text Solution

    |

  2. If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y...

    Text Solution

    |

  3. If a , b , c are distinct real numbers and the system of equations a x...

    Text Solution

    |

  4. If x , y , z are have not triavle solution such that a x+y+z=0 x+b y...

    Text Solution

    |

  5. Solve following system of homogeneous linear equations: x+y-2z=0,\ ...

    Text Solution

    |

  6. Solve following system of homogeneous linear equations: 2x+3y+4z=0,...

    Text Solution

    |

  7. Solve following system of homogeneous linear equations: 3x+y+z=0,\ ...

    Text Solution

    |

  8. Find the real values of lambda for which the following system of linea...

    Text Solution

    |

  9. If a , b , c are non-zero real numbers and if the system of equations ...

    Text Solution

    |

  10. If A is a singular matrix, then write the value of |A| .

    Text Solution

    |

  11. For what value of x , the matrix [[5-x,x+1] ,[2, 4]] is singular?

    Text Solution

    |

  12. Write the value of the determinant |[2, 3, 4], [5, 6, 8], [6x,9x,12x...

    Text Solution

    |

  13. State whether the matrix [[2,3 ],[6, 4]] is singular or nonsingula...

    Text Solution

    |

  14. Find the value of the determinant |[4200 ,4201], [4202, 4203]| .

    Text Solution

    |

  15. Find the value of the determinant |[101 ,102 ,103],[ 104 ,105 ,106],...

    Text Solution

    |

  16. Write the value of the determinant |[a,1,b+c], [b,1,c+a] ,[c,1,a+b]|...

    Text Solution

    |

  17. If A=[[0,i],[i,1]] and B=[[0, 1],[1, 0]] , find the value of |A|+|B| .

    Text Solution

    |

  18. If A=[[1, 2],[ 3,-1]] and B=[[1, 0],[-1 ,0]] , find |A B| .

    Text Solution

    |

  19. Evaluate: |[4785, 4787],[ 4789, 4791]| .

    Text Solution

    |

  20. If w is an imaginary cube root of unity, find the value of |[1,w, w^...

    Text Solution

    |