Home
Class 12
MATHS
Determine for that values of lambda and...

Determine for that values of `lambda and mu` the following system of equations
`x+y+xz=6,
x+2y+43z=10 and` x+2y+lambdaz=mu` have (i) no solution (iii) a unique solution ? (iii) an infine number of solution?

Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

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

    ALLEN|Exercise All Questions|147 Videos

Similar Questions

Explore conceptually related problems

. For what values of lambda and mu the system of equations x+y+z=6, x+2y+3z=10, x+2y+lambdaz=mu has (i) Unique solution (ii) No solution (iii) Infinite number of solutions

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.

For which value (s) of lambda , do the pair of linear equations lambdax + y = lambda^(2) and x + lambda y = 1 have (i) no solution ? (ii) infinitely many solutions ? (iii) a unique solution ?

For what values of p and q the system od equations x+y+z=6 x+2y+3z=10 x+2y+pz=q has (i) unique sollution ? (ii) an infinitely many solutions ? (iii) no solution ?

For what values of p and q, the system of equations 2x+py+6z=8,x+2y+qz=5,x+y+3z=4 has (i) no solution (ii) a unique solution (iii) infinitely many solutions.

The system of equations 3x+y-z=0, 5x+2y-3z=0, 15x+6y-9z=5 has (A) no solution (B) a unique solution (C) two distinct solutions (D) infinitely many solutions

For what values of a and b, the system of equations 2x+a y+6z=8, x+2y+b z=5, x+y+3z=4 has: (i) a unique solution (ii) infinitely many solutions (iii) no solution

For what values of p and q the system of equations 2x+py+6z=8, x+2y+qz=5, x+y+3z=4 has i no solution ii a unique solution iii in finitely many solutions.

For what values of p and q the system of equations 2x+py+6z=8, x+2y+qz=5, x+y+3z=4 has i no solution ii a unique solution iii in finitely many solutions.

The system of equations -2x+y+z=a , x-2y+z=b , x+y-2z=c , has: (a)no solution if a+b+c!=0 (b)unique solution if a+b+c=0 (c)infinite number of solutions if a+b+c=0 (d)none of these

ALLEN-DETERMINANTS-All Questions
  1. Solve the following sets of equation using Cramer’s rule and remark...

    Text Solution

    |

  2. Solve the following sets of equation using Cramers rule and remark a...

    Text Solution

    |

  3. Determine for that values of lambda and mu the following system of eq...

    Text Solution

    |

  4. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

    Text Solution

    |

  5. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  6. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

    Text Solution

    |

  7. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

    Text Solution

    |

  8. Using the properties of determinants, find the value of | 0 a -b ...

    Text Solution

    |

  9. Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"...

    Text Solution

    |

  10. If SS(r)=alpha^(r)+beta^(r)+gamma^(r)"then show that "=[{:(,S(0),S(1),...

    Text Solution

    |

  11. If a x1 2+b y1 2+c z1 2=a x1 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d\ a...

    Text Solution

    |

  12. If ∣ x - 2 -3 3x 2x ∣ =3, find the negative of integer va...

    Text Solution

    |

  13. If x,y and y are not all zero and if ax+by+cz=0,bx+cy+az=0 and cx...

    Text Solution

    |

  14. Prove that the system of equations in xa +y+z=0 , x +by +z=0 ,...

    Text Solution

    |

  15. If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1...

    Text Solution

    |

  16. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  17. If D=|(1, 1, 1), (1, 1+x, 1), (1, 1, 1+y)| for x!=0, y!=0 then D is (...

    Text Solution

    |

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

    Text Solution

    |

  19. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

    Text Solution

    |

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

    Text Solution

    |