Home
Class 12
MATHS
If S is the set of distinct values of...

If S is the set of distinct values of 'b' for which the following system of linear equations
`x+y+z=1`
`x+ay +z=1`
`ax+by+z=0`
has no solution then S is

A

an infinite set

B

a finite set containing two or more elements

C

a singleton

D

an empty set

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

If S is the set of distinct values of ' b for which the following system of linear equations x+y+z=1 x+a y+z=1 a x+b y+z=0 has no solution, then S is : a finite set containing two or more elements (2) a singleton an empty set (4) an infinite set

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

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial solution

If the system of linear equations x+ky+3z=0 3x+ky-2z=0 2x+4y-3z=0 has a non-zero solution (x,y,z) then (xz)/(y^2) is equal to

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.

Solve the following system of linear equations by Cramers rule: x+y=5,\ \ y+z=3,\ \ x+z=4

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

Solve the following system of linear equations using matrix method : 3x + y + z = 1, 2x + 2z =0, 5x + y + 2z = 0 .

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

The system of equations ax-y- z=a-1 ,x-ay-z=a-1,x-y-az=a-1 has no solution if a is:

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. Let A=[(1,0,0),(1,1,0),(1,1,1)] and B=A^20 . Then the sum of the elem...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If s={x in [0,2pi]:|[0,cosx,-sinx],[sinx,0,cosx],[cosx,sinx,0]|=0} the...

    Text Solution

    |

  5. The number of real values of for which the system of linear equation...

    Text Solution

    |

  6. Let A be any 3xx3 invertible matrix. Thenwhich one of the following i...

    Text Solution

    |

  7. For two 3xx3 matrices A and B, let A+B=2B' and 3A+2B=I3 where B' is t...

    Text Solution

    |

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

    Text Solution

    |

  9. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

    Text Solution

    |

  10. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Let A be a 3xx3 matrix such that A^2-5A+7I=0 then which of the stateme...

    Text Solution

    |

  13. If {:A=[(-4,-1),(3,1)]:}, then the determint of the matrix (A^2016-2A^...

    Text Solution

    |

  14. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  15. if A=[(1,2,3),(2,1,-1),(a,2,b)] is a matrix satisfying A A'=9l(3,) fin...

    Text Solution

    |

  16. if the value of the determinant |{:(a,,1,,1),(1,,b,,1),(1,,1,,c):}| ...

    Text Solution

    |

  17. If A=[(0,-1),(1,0)] , then which one of the following statements is n...

    Text Solution

    |

  18. If A is a 3 x 3 matrix such that |5-adjA|=5 , then |A| is equal to ...

    Text Solution

    |

  19. If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 t...

    Text Solution

    |

  20. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

    Text Solution

    |