Home
Class 12
MATHS
The equation [(1,2,2),(1,3,4),(3,4,k)]=[...

The equation `[(1,2,2),(1,3,4),(3,4,k)]=[(0),(0),(0)]` has a solution for (x, y, z) besides (0, 0, 0). Then the value of k is _________ .

Text Solution

Verified by Experts

The correct Answer is:
2
`|(1,2,2),(1,3,4),(3,4,k)|=0`
or `1(3k-16)-2(k-12)+2(4-9)=0`
or `3k-16-2k+24-10=0`
or `k=2`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise JEE Main Previous Year|11 Videos

  • MATRICES

    CENGAGE|Exercise JEE Advanced Previous Year|26 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

The equation [1 2 2 1 3 4 2 4k][x y z]=[0 0 0] has a solution for (x ,y ,z) besides (0,0,0)dot Then the value of k is _______.

If x=3k-2,y=2k is a solution of equation 4x-7y+12=0 then value of k is

If the system of equation 14x-3y+z=12, x-2y=0 and x+2z=0 has a solution (x_(0), y_(0), z_(0)) , then the value of x_(0)^(2)+y_(2)^(2)+z_(2)^(2) is equal to

If x=3k+2 and y = 2k-1 is a solution of the equation 4x-3y+1=0 , find the value of k.

The equations x+y-2z=0,2x-3y-z=0,x-5y+4z=k have non-zero solutions if k=

If x =3k-2 ; y =2k is a solution of equation 4x-7y+12=0 then find the value of k

The line (x)/(k)=(y)/(2)=(z)/(-12) makes an isosceles triangle with the planes 2x+y+3z-1=0 and x+2y-3z-1=0 then the value of k is-

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

CENGAGE-MATRICES-Exercise (Numerical)
  1. Let x be the solution set of equation A^x=Idot,w h e r eA+[0 1-1 4-3 4...

    Text Solution

    |

  2. A=[1t a n x-t a n x1]a n df(x) is defined as f(x)=d e tdot(A^T A^(-1))...

    Text Solution

    |

  3. The equation [(1,2,2),(1,3,4),(3,4,k)]=[(0),(0),(0)] has a solution fo...

    Text Solution

    |

  4. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

    Text Solution

    |

  5. Let A=[3x^2 1 6x],B=[abc],a n dC=[(x+2)^2 5x^2 2x5x^2 2x(x+2)^2 2x(x+2...

    Text Solution

    |

  6. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

    Text Solution

    |

  7. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

    Text Solution

    |

  8. Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r...

    Text Solution

    |

  9. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

    Text Solution

    |

  10. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

    Text Solution

    |

  11. If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I, t...

    Text Solution

    |

  12. If a, b, and c are integers, then number of matrices A=[(a,b,c),(b,c,a...

    Text Solution

    |

  13. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

    Text Solution

    |

  14. A square matrix M of order 3 satisfies M^(2)=I-M, where I is an identi...

    Text Solution

    |

  15. Let A=[a("ij")](3xx3), B=[b("ij")](3xx3) and C=[c("ij")](3xx3) be any ...

    Text Solution

    |

  16. If A is a square matrix of order 2xx2 such that |A|=27, then sum of th...

    Text Solution

    |

  17. If A is a aquare matrix of order 2 and det. A=10, then ((tr. A)^(2)-tr...

    Text Solution

    |

  18. Let A and B are two square matrices of order 3 such that det. (A)=3 an...

    Text Solution

    |

  19. Let P, Q and R be invertible matrices of order 3 such A=PQ^(-1), B=QR^...

    Text Solution

    |

  20. If A=[(1,x,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix B and d...

    Text Solution

    |