Home
Class 12
MATHS
The values of k in R for which the syst...

The values of `k in R` for which the system of equations `x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0` admits of nontrivial solution is a. `2` b. `5//2` c. `3` d. `5//4`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

Find the value of lambda for which the homogeneous system of equations: 2x+3y-2z=0 , 2x-y+3z=0 , 7x+lambday-z=0 has non-trivial solutions.

Find the real values of a for which the system of equations a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0 x+y+z=0 has a non -zero solution.

The system of equations lambdax+y+3z=0,2x+muy-z=0,5x+7y+z=0 has infinitely many solutions in R. Then

If the system of equations x+2y+3z=1, 2x+ky+5z=1, 3x+4y+7z=1 has no solutions, then -

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are a. -1,2 b. 1,2 c. 0,1 d. -1,1

If the system of equations x+y+z=6, x+2y+kz=0 and x+2y+3z=10 has no solution, then the value of k is -

Solve the following system of homogeneous equations. x+2y-z=0,x-2y+2z=0,x+z=0

The system of equation x+y+2z=1, x+2y+3z=2, x+4y+alphaz=4 . Has unique then

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If determinant |[cos(theta+phi),-sin(theta+phi),cos2phi],[sin theta,co...

    Text Solution

    |

  2. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

    Text Solution

    |

  3. The values of k in R for which the system of equations x+k y+3z=0,k x...

    Text Solution

    |

  4. A determinant of second order is made with the elements 0 and 1. Fi...

    Text Solution

    |

  5. If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, ...

    Text Solution

    |

  6. Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[...

    Text Solution

    |

  7. Consider the determinant f(x)=|[0,x^2-a, x^3-b], [x^2+a,0,x^2+c], [x^4...

    Text Solution

    |

  8. Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

    Text Solution

    |

  9. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

    Text Solution

    |

  10. If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a ...

    Text Solution

    |

  11. Each question has four choices a, b, c and d, out of which only one is...

    Text Solution

    |

  12. If a ,b ,c in R , then find the number of real roots of the equat...

    Text Solution

    |

  13. Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by ...

    Text Solution

    |

  14. Without expanding at any stage, prove that the value of each of the...

    Text Solution

    |

  15. If a,b c(all positive)are the p th,q thand r th terms repectively of a...

    Text Solution

    |

  16. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

    Text Solution

    |

  17. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

    Text Solution

    |

  18. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

    Text Solution

    |

  19. If a1b1c1,a2b2c2 and a3b3c3 are three digit even natural numbers and ...

    Text Solution

    |

  20. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

    Text Solution

    |