Home
Class 12
MATHS
The set of the all values of lamda for w...

The set of the all values of `lamda` for which the system of linear equations
`2x_(1) - 2x_(2) + x_(3) = lamdax_(1)`
`2x_(1) - 3x_(2) + 2x_(3) = lamda x_(2)`
`-x_(1) + 2x_(2) = lamda x_(3)` has a non-trivial solution,

A

is an empty set

B

is a singleton

C

contains two elements

D

contains more than two elements

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos
  • MATRICES & DETERMINANT

    RESONANCE|Exercise EXERCISE-3|31 Videos
  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos
  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

The set of all values of lambda for which the system of linear equations: 2x_(1)-2x_(2)+x_(3)=lambda x_(1)2x_(1)-3x_(2)+2x_(3)=lambda x_(2) has a non-trivial solution,(1) is an empty set (2) is a singleton ( 3) contains two elements (4) contains more than two elements

Consider the system of linear equations: x_(1) + 2x_(2) + x_(3) = 3 2x_(1) + 3x_(2) + x_(3) = 3 3x_(1) + 5x_(2) + 2x_(3) = 1 The system has

The system of linear equations x_(1)+2x_(2)+x_(3)=3, 2x_(1)+3x_(2)+x_(3)=3 and 3x_(1)+5x_(2)+2x_(3)=1 , has

Let lambda in R . The system of linear equations 2x_(1) - 4x_(2) + lambda x_(3) = 1 x_(1) -6x_(2) + x_(3) = 2 lambda x_(1) - 10x_(2) + 4 x_(3) = 3 is inconsistent for :

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

RESONANCE-MATRICES & DETERMINANT-PART-II:
  1. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  2. Statement -1 : Determinant of a skew-symmetric matrix of order 3 is ze...

    Text Solution

    |

  3. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

    Text Solution

    |

  4. Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q...

    Text Solution

    |

  5. The number of values of k, for which the system of eauations: (k+1)x...

    Text Solution

    |

  6. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3 x 3 matrix ...

    Text Solution

    |

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

    Text Solution

    |

  8. If A is an 3xx3 non-singular matrix such that AA^'=""A^' A and B""=...

    Text Solution

    |

  9. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

  10. The set of the all values of lamda for which the system of linear equa...

    Text Solution

    |

  11. The system of linear equations: x+lambday-z=0 lamdax-y-z=0 x+y-l...

    Text Solution

    |

  12. If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T), then 5a+b is equal to

    Text Solution

    |

  13. If S is the set of distinct values of ' b for which the following syst...

    Text Solution

    |

  14. If A=|{:(,2,-3),(,-4,1):}| then adj (3A^(2)+12A) is equal to

    Text Solution

    |

  15. If the system of linear equations x+ky+3z=0 3x+ky-2z=0 2x+4y-3z=0 ...

    Text Solution

    |

  16. If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordere...

    Text Solution

    |

  17. The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2...

    Text Solution

    |

  18. If A=[(costheta, -sin theta ),(sin theta, cos theta) ] , then the ma...

    Text Solution

    |

  19. Let d in R, and A= [{:(-2, " "4+d,("sin"theta)-2),(1, ("sin"theta)...

    Text Solution

    |

  20. Let A=|{:(,0,21,r),(,p,q,-r),(,p,-q,r):}|=A A^(T)=I(3) then |p| is

    Text Solution

    |