Home
Class 12
MATHS
Find all values of lambda for which the ...

Find all values of `lambda` for which the `(lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0` possess non-trivial solution and find the ratios `x:y:z,` where `lambda` has the smallest of these value.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|2 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Find all values of lambda for which the (lambda-1)x+(3 lambda+1)y+2 lambda z=0(lambda-1)x+(4 lambda-2)y+(lambda+3)z=02x+(3 lambda+1)y+3(lambda-1)z possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find the values of lambda for which 3-lambda,-1,1-1,5-lambda,-11,-1,3-lambda]|=0

The system of equations lambda x+(lambda+1)y+(lambda-1)z=0,(lambda+1)x+lambda y+(lambda+z)z=0,(lambda-1)x+(lambda+2)y+lambda z= bas a non-trivial solutions for

Find values of lambda for which line y=x+1,y=lambda x+2 and y=(lambda^(2)+lambda-1)x+3 are con-current.

The sum of distinct value of lambda for which the system of equations (lambda -1 )x + (3lambda + 1) y + 2 lambda x= 0 (lambda -1) x + (4lambda - 2) y + (lambda + 3) x= 0 2x + (2lambda + 1) y + 3(lambda - 1) z=0 has non - zeor solutions is ______.

Find values of lambda for which line y=x+1,y=2x+2 and y=(lambda^(2)+lambda-1)x+3 are con-current.

The sum of possible value of lambda for which the system of equations (lambda+1)x+8y=4 lambda and lambda x+(lambda+3)y=3 lambda-1 is inconsistent is

The value(s) of lambda for which the system of equations (1-lambda)x+3y-4z=0 x-(3+lambda)y + 5z=0 3x+y-lambdaz=0 possesses non-trivial solutions .

The plane 2x-(1+lambda)y+3 lambda z=0 passes through the intersection of the plane

The set of all values of lambda for which the systme of linear equations x-2y-2z = lambda x, x +2y +z = lambda y " and "-x-y = lambdaz has a non-trivial solution.

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lamb...

    Text Solution

    |

  2. If a^(2)+b^(2)+c^(2)=-2 and f(x)= |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x...

    Text Solution

    |

  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

    Text Solution

    |

  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. 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

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k which the linear equations 4x+ky+2z=0 kx...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. The set of the all values of lamda for which the system of linear equa...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

    Text Solution

    |

  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

    Text Solution

    |

  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

    Text Solution

    |

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

    Text Solution

    |