Home
Class 12
MATHS
The values of a for which the system of ...

The values of a for which the system of equations `x+y+z=0, x+ay+az=0` and `x-ay+z=0`, possesses non-zero solutions, are given by

A

1,2

B

1,-1

C

1,0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
The given system of equations posses non -zero solutions.
`:.|(1,1,1),(1,a,a),(1,-a,1)|=0`
Applying `R_(2)toR_(2)-R_(1)` and `R_(3)-R_(3)-R_(1)`
`implies|(1,1,1),(0,a-1,a-1),(0,-a-1,0)|=0implies1(0-(a^(2)-1))=0`
`impliesa^(2)=1impliesa=+-1`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MISCELLANEOUS PROBLEMS|49 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

The values of k for which the system of equations kx+y+z=0,x-ky+z=0 and x+y+z=0 possesses non-trivial solution. Are

The values of k for which the system of equations kx+y+z=0,x-ky+z=0,x+y+z=0 posseses non zero solutions is given by

Values of k for which the system of equation x+ky+3z=0, kx+2y+2z=0 and 2x+3y+4z=0 possesses non-trivial solution

The value of a for which the system of linear equations ax+y+z=0,ay+z=0,x+y+z=0 possesses non-trivial solution is

The value of for which the system of equations ax +y+z=0,x+ay+z=0,x+y+z=0 possess a non-null solution is

The value of a for whch the sytem of equations x+ay+z=1 ax+y+z=1 x+y+az=1 has no solution is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MHT CET CORNER
  1. The values of a for which the system of equations x+y+z=0, x+ay+az=0 a...

    Text Solution

    |

  2. If A=[(1,1,0),(2,1,5),(1,2,1)] then a(11)A(21)+a(12)A(22)+a(13)A(23) i...

    Text Solution

    |

  3. If A=[(2,2),(-3,2)], B=[(0,-1),(1,0)] then (B^(-1)A^(-1))^(-1) is equa...

    Text Solution

    |

  4. If matrix A=[(1,2),(4,3)], such that AX=l, then X is equal to

    Text Solution

    |

  5. The multiplicative inverse of A = [(cos theta,-sin theta),(sin theta,c...

    Text Solution

    |

  6. The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0...

    Text Solution

    |

  7. Let A=[(cos theta, -sin theta),(- sin theta,-cos theta)] then the inve...

    Text Solution

    |

  8. If matrix A=[(a,b),(c,d)], then |A|^(-1) is equal to

    Text Solution

    |

  9. If A=[(3,2,4),(1,2,1),(3,2,6)] and A(ij) are the cofactors of a(ij), t...

    Text Solution

    |

  10. A=[(cos theta, -sin theta),(sin theta, cos theta)] and AB=BA=l, then B...

    Text Solution

    |

  11. The inverse matrix of A=[(0,1,2),(1,2,3),(3,1,1)] is

    Text Solution

    |

  12. The solutiion of (x,y,z) the equation [(-1,0,1),(-1,1,0),(0,-1,1)][(x)...

    Text Solution

    |

  13. For the system of equaltions : x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

    Text Solution

    |

  14. If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2...

    Text Solution

    |

  15. If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then the ...

    Text Solution

    |

  16. If A=[(1,-1),(2,-1)] and B=[(1,a),(4,b)] and (A+B)^(2)=A^(2)+B^(2). ...

    Text Solution

    |

  17. If A+I=[(3,-2),(4,1)] then (A+I)(A-I) is equal to

    Text Solution

    |

  18. If A=[(x,y,z)],B=[(a,h,g),(h,b,f),(g,f,c)] and C=[(x),(y),(z)] Then ...

    Text Solution

    |

  19. If A=[(-2,4),(-1,2)] then A^(2) is equal to

    Text Solution

    |