Home
Class 12
MATHS
Solve the system of the equations: a x+b...

Solve the system of the equations: `a x+b y+c z=d` `a^2x+b^2y+c^2z=d^2` `a^3x+b^3y+c^3z=d^3` Will the solution always exist and be unique?

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

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

Examine the consistency of the system of equations 3x-y -2z =2 2y - z =-1 3x- 5y =3

Solve system of linear equations , using matrix method 2x+ 3y + 3z=5 x-2y +z=-4 3x-y-2z=3

Solve the following system of equations by matrix method. 3x-2y+3z=8 2x+ y-z=1 4x-3y +2z =4

Solve the following system of homogeneous equations. 3x+2y+7z=0,4x-3y-2z=0, 5x+9y+23z=0

CENGAGE-DETERMINANTS-All Questions
  1. If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^...

    Text Solution

    |

  2. If |x^n x^(n+2)x^(n+3)y^n y^(n+2)y^(n+3)z^n z^(n+2)z^(n+3)|=(x-y)(y-z)...

    Text Solution

    |

  3. Solve the system of the equations: a x+b y+c z=d a^2x+b^2y+c^2z=d^2 a^...

    Text Solution

    |

  4. if |{:(a,,b-c,,c+b),(a+c,,b ,,c-a),(a-b,,a+b,,c):}|=0 then the line ...

    Text Solution

    |

  5. If 2a x-2y+3z=0,x+a y+2z=0,a n d2+a z=0 have a nontrivial solution,...

    Text Solution

    |

  6. If |.| denotes the greatest integer less than or equal to the real num...

    Text Solution

    |

  7. if (x) =a +bx+cx^(2)" and " alpha, beta gamma are the roots of the ...

    Text Solution

    |

  8. If x ,ya n dz are not all zero and connected by the equations a1x+b...

    Text Solution

    |

  9. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

    Text Solution

    |

  10. If p ,q ,r are in A.P. then value of determinant |a^2+2^(n+1)+2p b^2+2...

    Text Solution

    |

  11. For what values of k , the following system of equations possesses ...

    Text Solution

    |

  12. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

    Text Solution

    |

  13. Solve by Cramers rule x+y+z=6 x-y+z=2 3x+2y-4z=-5

    Text Solution

    |

  14. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

    Text Solution

    |

  15. Find the value of aa n db if the system of equation a^2x-b y=a^2-ba...

    Text Solution

    |

  16. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

    Text Solution

    |

  17. f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)(xvec0)(f(x))/x ...

    Text Solution

    |

  18. If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x...

    Text Solution

    |

  19. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

    Text Solution

    |

  20. If |a^2+lambda^2a b+clambdac a-blambdaa b-clambdab^2+lambda^2b c+...

    Text Solution

    |