Home
Class 12
MATHS
If the system of linear equations x1+2x2...

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

Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    ALLEN|Exercise EX -JA|8 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    ALLEN|Exercise All Questions|145 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_(1)+5x_(2)+ax_(3)=b, is consistent and has infinite number of solutions,then :-

Given a system of equations in x,y,z : x+y+z=6,x+2y+3z=10 and x+2y+az=b . If this system has infinite number of solutions, then a^(2)+b= ……….

Show that the following systems of linear equations has infinite number of solutions and solve x+2y=5,\ \ 3x+6y=15

Determine conditions on a, b and c so that x_(1)+2x_(2)+3x_(3)=a 4x_(1)+5x_(2)+6x_(3)=b 7x_(1)+8x_(2)+9x_(3)=c will have no solutions or have an infinite number of solution.

Show that the system of equations. " " 2 x - 3y = 5, 6x - 9y = 15 . has an infinite number of solutions.

Number of real solutions of the equation |x-1|+|x-3|=(3)/(2) is

The number of real solutions of the equation |x|^(2)-3|x|+2=0 is (1982,1M)4(b)1(c)3 (d) 2

ALLEN-DETERMINANTS-All Questions
  1. If D=|1 1 1 1 1+x1 1 1 1+y|"f o r"x!=0, y!=0 then D is (1) divisibl...

    Text Solution

    |

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

    Text Solution

    |

  3. Let a, b, c be such that b(a""+""c)!=0 . If |a a+1a-1-bb+1b-1cc-1c...

    Text Solution

    |

  4. Consider the system of linear equations; x-1\ +2x2+x3=3 2x1+3x2+3=3 3x...

    Text Solution

    |

  5. The number of value of k for which the linear equations 4x+k y+2z=0k x...

    Text Solution

    |

  6. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

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

    Text Solution

    |

  8. If a ,b ,c are sides of a scalene triangle, then value of |a b c b c a...

    Text Solution

    |

  9. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

    Text Solution

    |

  10. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

    Text Solution

    |

  11. Consider the system of equations x+a y=0,\ y+a z=0.\ Then the set of ...

    Text Solution

    |

  12. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

    Text Solution

    |

  13. The set of all values of lamda for which the system of linear equation...

    Text Solution

    |

  14. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

    Text Solution

    |

  15. The number of distinct real roots of the equation |cosx s in x s in x ...

    Text Solution

    |

  16. Test the consistency and solve them when consistent the following s...

    Text Solution

    |

  17. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

    Text Solution

    |

  18. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  19. The value of lambda for which the system of equations 2x-y-z=12,x-2y +...

    Text Solution

    |

  20. Consider the system of equations x-2y+3z=1;-x+y-2z=; x-3y+4z=1. State...

    Text Solution

    |