Home
Class 12
MATHS
Consider the system of equations x+y+...

Consider the system of equations
`x+y+z=6`
`x+2y+3z=10`
`x+2y+lambdaz =mu`
the system has unique solution if

A

`lamda=3, mu=10`

B

`lamda!=,mu=10`

C

`lamda!=3,mu!=10`

D

`lamda=3, mu!=10`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `x+y+z=6,x+2y+3z=10`
and `x+2y+lamdaz=mu`
For no solution `A=|(1,1,1),(1,2,3),(1,2,lamda)|=0`
`implies1(2 lamda=6)-1(lamda-3)+1(2-2)=0`
`implieslamda-3=0implieslamda=3`
`[(2lamda-6,-(lamda-2),1),(-(lamda-3),lamda-1,-2),(0,1,1)][(6),(10),(mu)]!=[(0),(0),(0)]`
`implies[(12 lamda-36, -10lamda+20, +mu),(-6lamda+18xx, 10 lamda-10,-2mu),(0+10,+mu, )]!=[(0),(0),(0)]`
`implies[(2lamda-16+mu),(4 lamda+8-2mu),(10+mu)]!=[(0),(0),(0)]`
`implies2lamda-16+mu!=0`
`=2xx3-16+mu!=0`
`implies mu!=10`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATHEMATICAL LOGIC

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|22 Videos

  • MHTCET 2007

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambdaz =mu The system has no solution if

Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambdaz =mu the system has infinite solutions if

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

If the system of linear equations x+y+z=6, x+2y+3z=14 and 2x +5y+ lambdaz=mu(lambda,mu ne R) has a unique solution if lambda is

Consider the system of equation x+y+z=6,x+2y+3z=10, and x+2y+lambda z=mu Statement 1: if the system has infinite number of solutions,then mu=10. Statement 2: The determinant det[[1,2,101,2,101,2,mu]]=0 for mu=10

Consider the system of equation x+2y-3z=a , 2x+6y-11z=b , x-2y+7c then

Consider the system of equations x+y+z=5, x+2y+3z=9, x+3y+ lambda z=mu The sustem is called smart brilliant good and lazy according as it has solution unique solution infinitely many solution respectively . The system is smart if

Consider the system of equations x+y+z=5, x+2y+3z=9, x+3y+ lambda z=mu The sustem is called smart brilliant good and lazy according as it has solution unique solution infinitely many solution respectively . The system is good if

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MISCELLANEOUS PROBLEMS
  1. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

    Text Solution

    |

  2. If A(theta)=[(1, than theta),(-tan, theta=1)] and AB=l, then (sec^(2)t...

    Text Solution

    |

  3. If A=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha,0),(0,0,1)] the...

    Text Solution

    |

  4. Suppose A is a matrix of order 3 and B=|A|A^(-1). If |A|=5, then |B| i...

    Text Solution

    |

  5. if[{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}],"then" A=?

    Text Solution

    |

  6. If f(theta)=[(cos theta, -sin theta,0),(sin theta, cos theta, 0),(0,0,...

    Text Solution

    |

  7. If A is a singular matrix, then Aadj(A) is a/an

    Text Solution

    |

  8. If k is a scalar and l is a unit matrix of order 3 then adj(kl) is equ...

    Text Solution

    |

  9. Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambda...

    Text Solution

    |

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

    Text Solution

    |

  11. Let a, b, c be positive real numbers. The following system of equation...

    Text Solution

    |

  12. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  13. The symmetric part of the matrix A=[(1,2,4),(6,8,2),(2,-2,7)] is equal...

    Text Solution

    |

  14. If {:A=[(1,0,0),(0,1,0),(a,b,-1)]:}, then A^2 is equal to

    Text Solution

    |

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

    Text Solution

    |

  16. If A is a 3xx3 such that |5.adj(A)|=5 then |A| is equal to

    Text Solution

    |

  17. If A=[(alpha, 2),(2, alpha)] and |A^(3)|=27 then alpha is equal to

    Text Solution

    |

  18. The elements in the first row and third column of the inverse of the m...

    Text Solution

    |

  19. If A=[(-1,3),(2,1)] then 1+A+A^(2)+…………..+oo is equal to

    Text Solution

    |

  20. if A=[[1,-2] , [4,5]] and f(t)=t^2-3t+7 then f(A)+[[3,6],[-12,-9]]=

    Text Solution

    |