Home
Class 12
MATHS
The set of all values of lambda for wh...

The set of all values of `lambda` for which the system of linear equations : `2x_1-2x_2+""x_3=lambdax_1` `2x_1-3x_2+""2x_3=lambdax_2` `-x_1+""2x_2=lambdax_3` has a non-trivial solution, (1) is an empty set (2) is a singleton (3) contains two elements (4) contains more than two elements

A

contains two elements.

B

contains more than two elements

C

is an empty set.

D

is a singleton

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -1 CONCEPT BUILDER|65 Videos

  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -2 CONCEPT APPLICATOR|30 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

  • DIFFERENTIAL EQUATIONS

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

The set of all values of lambda for which the system of linear equations: 2x_(1)-2x_(2)+x_(3)=lambda x_(1)2x_(1)-3x_(2)+2x_(3)=lambda x_(2) has a non-trivial solution,(1) is an empty set (2) is a singleton ( 3) contains two elements (4) contains more than two elements

The set of all values of lambda for which the system of linear equations: x-2y-2z=lambda x,x+2y+z=lambda y and -x-y=lambda z has a non-trivial solution: (a) is an empty sheet (b) is a singleton (c) contains more than two elements (d) contains exactly two elements

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

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.

If f(x)+2f(1/x)=3x , x!=0, and S={x in R :f(x)=f(-x)} ; then S: (1) is an empty set. (2) contains exactly one element. (3) contains exactly two elements. (4) contains more than two elements

Let lambda in R , the system of linear equation 2x_1-4x_2+lambdax_3=1 x_1-6x_2+x_3=2 lambda x_1-10x_2+4x_3=3 is inconsistant. Find the value of lambda .

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 :

DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR
  1. The set of all values of lambda for which the system of linear equat...

    Text Solution

    |

  2. The coefficient of x in f (x) = |{:(x , 1 + sin x , cos x ),(1 , lo...

    Text Solution

    |

  3. If a(n)=(1)/(n+1)+1 then find the vaue of a(1)+a(3)+a(5)

    Text Solution

    |

  4. If [] denotes the greatest integer less than or equal to the real numb...

    Text Solution

    |

  5. Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx...

    Text Solution

    |

  6. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

    Text Solution

    |

  7. If m is a positive integer and Dr=|2r-1\ ^m Cr1m^2-1 2^m m+1s in^2(...

    Text Solution

    |

  8. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

    Text Solution

    |

  9. If omega is a non-real cube root of unity, then Delta = |(a(1) + b(1) ...

    Text Solution

    |

  10. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

    Text Solution

    |

  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  12. If |{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

    Text Solution

    |

  13. The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2)...

    Text Solution

    |

  14. The value of the determinant |{:(1 ,(5^(2x)-5^(-2x))^(2),(5^(2x)-5^(-2...

    Text Solution

    |

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

    Text Solution

    |

  16. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

    Text Solution

    |

  17. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

    Text Solution

    |

  18. If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...

    Text Solution

    |

  19. the value of the determinant |{:((a(1)-b(1))^(2),,(a(1)-b(2))^(2),,...

    Text Solution

    |

  20. f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The val...

    Text Solution

    |

  21. If the matrix A = [{:(y+a,b,c),(a,y+b,c),(a,b,y+c):}] has rank 3, then

    Text Solution

    |