Home
Class 12
MATHS
Test the consistency and solve them when...

Test the consistency and solve them when consistent the following system of equations for all values of `lambda:` `x+y+z=1` `x+3y-2z=lambda` `3+(lambda+2)y-3z=2lambda+1`

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

Determine the values of lambda for which the following system of equations fail to have a unique solution: lambda x+3y-z=1,x+2y+z=2,-lambda x+y+2z=-1

The value of lambda , such that the following system of equations has no solution, is x - 2y + z = - 4 2x - y - 2z = 2 x + y + lambda z = 4

Determine the values of lambda for which the following system of equations: lambda x+3y-z=1x+2y+z=2-lambda x+y+2z=-1 has non-trival solutions.

Find the real values of lambda for which the following system of linear equations has non- trivial solutions.Also,find the non-trivial solutions.2 lambda x-2y+3z=0x+lambda y+2z=02x+lambda z=0

For which value of lambda , plane 4x + 6y -2z =8 and 2x+3y+ lambda z= 12 are parallel?

A system of equations lambda x+y+z=1,x+lambda y+z=lambda,x+y+lambda z=lambda^(2) have no solution then value of lambda is

The system of linear equations lambda x + y + z = 3 x - y - 2z = 6 -x + y + z = mu has

The sum of distinct value of lambda for which the system of equations (lambda -1 )x + (3lambda + 1) y + 2 lambda x= 0 (lambda -1) x + (4lambda - 2) y + (lambda + 3) x= 0 2x + (2lambda + 1) y + 3(lambda - 1) z=0 has non - zeor solutions is ______.

Test the consistency of the system x-y+2z=1,x+y+z=3,x-3y+3z=-1,2x+4y+z Also find the solution,if any

ALLEN-DETERMINANTS-All Questions
  1. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. The number of distinct real roots of the equation |cosx s in x s in x ...

    Text Solution

    |

  16. Test the consistency and solve them when consistent the following s...

    Text Solution

    |

  17. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

    Text Solution

    |

  18. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  19. The value of lambda for which the system of equations 2x-y-z=12,x-2y +...

    Text Solution

    |

  20. Consider the system of equations x-2y+3z=1;-x+y-2z=; x-3y+4z=1. State...

    Text Solution

    |