Home
Class 12
MATHS
The equation [[1, 2 ,2 ],[1 ,3, 4],[ 2, ...

The equation `[[1, 2 ,2 ],[1 ,3, 4],[ 2, 4,k]][(x) ,(y), (z)] =[(0),(0), (0)]` has `a` solution for `(x ,y ,z)` besides `(0,0,0)dot` 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

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If [(x+y,2x+z),(x-y,2z+w)]=[(4,7),(0,10)] then the values of x, y, z and w are -

If x = 2k + 1 and y = k is a solutions of the equation 5x + 3y - 7 = 0, find the value of k.

|{:(x,z,0),(0,y,y),(z,0,x):}|

x - 1 = 0 is the equation of directrix of the parabola y^(2) - kx + 8 = 0 . Then the value of k is _

If {:[(1,4),(2,0)]={:[(x,y^2),(z,0)] , ylt0 then x-y+z is equal to___

If R ={ (x,y) : x,y in z, x^(2) +y^(2) le 4 } is a relation on Z Z then domain of R is { 0,-1,k,-2,2} find the value of k.

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 -

If the equation of the tangent to the circle x^(2) + y^(2) - 2x + 6y - 6 =0 parallel to the line 3x - 4y +7 =0 is 3x - 4y +k=0 , then the value of k is-

If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solution, find the value of adot

|{:(" "0," "x,y),(-x," "0,z),(-y,-z,0):}|=0

CENGAGE PUBLICATION-MATRICES-All Questions
  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=[[1,t a n x],[-t a n x,1]] \ a n d \ f(x) is defined as f(x)=d e t(A...

    Text Solution

    |

  3. The equation [[1, 2 ,2 ],[1 ,3, 4],[ 2, 4,k]][(x) ,(y), (z)] =[(0),(0)...

    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(i j)])(3xx3) be a matrix such that AA^T=4Ia n da(i j)+2c(i j...

    Text Solution

    |

  8. Let S be the set which contains all possible values of l ,m ,n ,p ,q ,...

    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 square 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 P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix A a...

    Text Solution

    |