Home
Class 12
MATHS
If the system of linear equations x1 + 2...

If the system of linear equations `x_1 + 2x_2 + 3x_3 = 6, x_1 + 3x_2 + 5x_3 = 9, 2x_1 + 5x_2 + ax_3=b` , is consistent and has infinite number of solutions, then :-

A

a = 8 ,b can be any real number

B

b= 15 a can be any real number

C

a = `in` R - {8} and b `in` R - {15}

D

a=8 ,b=15

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B -Architecture Entrance Examination Papers|22 Videos
  • MATRICES

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Numerical Answer Type Questions)|20 Videos
  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos
  • PARABOLA

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTRE ENTRANCE EXAMINATION PAPERS|9 Videos

Similar Questions

Explore conceptually related problems

If the system of linear equations x_1+2x_2+3x_3=6,\ x_1+3x_2+5x_3=9,\ 2x_2+5x_2+a x_3=b is consistent and has infinite number of solutions, then- a in R-{8}a n d\ b in R-{15} a=8,\ b can be any real number a=8,\ b=15 b=15 ,\ a can be any real number

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

Consider the system of linear equations; x-1\ +2x_2+x_3=3 2x_1+3x_2+_3=3 3x_1+5x_2+2x_3=1 The system has Infinite number of solutions Exactly 3 solutions A unique solution No solution

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 :

MCGROW HILL PUBLICATION-MATRICES-Questions from Previous Years. AIEEE /JEE Main Papers
  1. If P=[[1, alpha, 3], [1, 3, 3], [2, 4, 4]] is the adjoint of 3times3 m...

    Text Solution

    |

  2. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  3. If the system of linear equations x1 + 2x2 + 3x3 = 6, x1 + 3x2 + 5x3 =...

    Text Solution

    |

  4. If p, q, r are 3 real number satisfying the matrix equation, [p q r][[...

    Text Solution

    |

  5. Consider the system of equations : x + ay = 0, y + az = 0 and z + ax=0...

    Text Solution

    |

  6. let A ={{:({:(a(11),a(12)),(a(21),a(22)):}):a(ij){0,1,2} and a(11)=a(2...

    Text Solution

    |

  7. The matrix A^2 + 4 A-5I, where I is identity matrix and A = [[1,2],[4,...

    Text Solution

    |

  8. Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , whe...

    Text Solution

    |

  9. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

    Text Solution

    |

  10. If B is a 3xx3 matrics such that B^2=0 then det[(1+B)^(50)-50B]=0

    Text Solution

    |

  11. Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),...

    Text Solution

    |

  12. If A=[(1,2,x),(3,-1,2)] and B=[(y),(x),(1)] be such that AB=[(6),(8)],...

    Text Solution

    |

  13. Let A and B be any two 3xx3 matrices . If A is symmetric and B is skew...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. If A = [(0,-1),(1,0)] then which one of the following statement is not...

    Text Solution

    |

  17. If A=[5a-b3 2] and A adj A=AA^T , then 5a+b is equal to: (1) -1 (2) ...

    Text Solution

    |

  18. If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]] and Q=PAP^T, ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |