Home
Class 12
MATHS
Let a,lambda,mu in R, Consider the syste...

Let `a,lambda,mu in R,` Consider the system of linear equations `ax+2y=lambda 3x-2y=mu` Which of the flollowing statement (s) is (are) correct?

A

if a=-3, then the system has infenitely many solutions for all values of `lambda and mu`

B

If `a ne 3`, then the system has a unique solutions for all values of `lambda and mu`

C

If `lambda+mu=0`,then the system has infenitely many solutions for all values of a=-3

D

If `lambda+mu=-0`,then the system has no solutions for a=-3

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise PART-II:|28 Videos
  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos
  • MATRICES & DETERMINANT

    RESONANCE|Exercise PART-IV|6 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

Let a,lambda,mu in R, Consider the system of linear equations ax+2y=lambda3x-2y=mu Which of the flollowing statement (s) is (are) correct?

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

Consider the system of equations x+y+z=5 x+2y+lamda^2z=9 x+3y+lamdaz=mu

System of equation x+3y+2z=6;x+lambda y+2z=7;x+3y+2z=mu has

The value of lambda and mu for which the system of linear equation x+y+z=2 x+2y+3z=5 x+3y+lambda z= mu has infinitely many solutions are , respectively :

The system of equations 3x-2y+z=0,lambda x-14y+15z=0,x+2y-3z=0 has non- zero solution then lambda=

Consider the system of linear equations x+y+z=5 , x+2y+lambda^(2)z=9,x+3y+lambda z=mu ,where lambda,mu in R .Then,which of the following statement is NOT correct?

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

If the system of linear equations x+2y+3z=lambda x, 3x+y+2z=lambday , 2x+3y+z=lambdaz has non trivial solution then lambda=

If the system of equations x+y+z=6, x+2y+lambdaz=10 and x+2y+3z=mu has infinite solutions, then the value of lambda+2mu is equal to

RESONANCE-MATRICES & DETERMINANT-EXERCISE-3
  1. Let a, b and c be three real number satisfying [a,b,c]|{:(,1,9,7),(,...

    Text Solution

    |

  2. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  3. Let M be a 3xx3 matrix satisfying M |{:(,0),(,1),(,0):}|=|{:(,-1),(,2...

    Text Solution

    |

  4. Let P=[a]"be a "3xx3 matrix and let Q=[b]=2^(i+j)a(i) "for" 1 lei, j l...

    Text Solution

    |

  5. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  6. If the adjoint of a 3 xx 3 matrix P is [{:(,1,4,4),(,2,1,7),(,1,1,3):}...

    Text Solution

    |

  7. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  8. Let M be a 2 x 2 symmetric matrix with integer entries . Then , ...

    Text Solution

    |

  9. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

    Text Solution

    |

  10. Let Xa n dY be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices...

    Text Solution

    |

  11. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  12. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  13. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

    Text Solution

    |

  14. Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...

    Text Solution

    |

  15. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

    Text Solution

    |

  16. Which of the following is (are) NOT the square of a 3xx3 matrix with r...

    Text Solution

    |

  17. For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alp...

    Text Solution

    |

  18. How many 3xx3 matrices M with entries from {0,1,2} are there, for whic...

    Text Solution

    |

  19. Let S be the set of all column matrices [(b(1)), (b(2)), (b(3))] such ...

    Text Solution

    |

  20. Let P be a matrix of order 3xx3 such that all the entries in P a...

    Text Solution

    |