Home
Class 12
MATHS
Let A=([a(i j)])(3xx3) be a matrix such ...

Let `A=([a_(i j)])_(3xx3)` be a matrix such that `AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j)` is the cofactor of `a_(i j)a n dI` is the unit matrix of order 3. `|a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0` then the value of `10lambda` is _______.

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 [(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))]=[(1,2,3),(2,3,4),(3,4,5)][(-1,-2),(-2,0),(0,-4)][(-4,-5,-6),(0,0,1)] , then the value of a_(22) is -

If a_(1),a_(2)a_(3),….,a_(15) are in A.P and a_(1)+a_(8)+a_(15)=15 , then a_(2)+a_(3)+a_(8)+a_(13)+a_(14) is equal to

If A=[a_(ij)] is a 2xx2 matrix such that a_(ij)=i+2j then A will be___

If a_(1), a_(2), a_(3), …., a_(n) are in H.P., prove that, a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) +…+ a_(n-1)a_(n) = (n-1)a_(1)a_(n)

If a_(1), a_(2), a_(3),…, a_(n) be in A.P. Show that, (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) +….+(1)/(a_(n-1)a_(n)) = (n-1)/(a_(1)a_(n))

If A = [a_(ij)] is a 2 xx2 matrix such that a_(ij)=i+2j , then A will be

If a_(r)= (cos 2r pi + i sin 2r pi)^(1/9) . Then the value of |(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)),(a_(7),a_(8),a_(9))| is

If a_(1), a_(2) , a_(3),…,a _(n+1) are in A. P. then the value of (1)/(a _(1)a_(2))+(1)/(a_(2)a_(3))+(1)/(a_(3)a_(4))+...+(1)/(a_(n)a_(n+1)) is-

If A=[a_(ij)] is a 3xx2 matrix whose elements are given by a_(ij)=3i-2j , then A will be__

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[...

    Text Solution

    |

  6. For two unimodular complex number z1a n dz2 [[barz1, -z2], [barz2, z1...

    Text Solution

    |

  7. If Aa n dB are two non-singular matrices of the same order such that B...

    Text Solution

    |

  8. If A is non-diagonal involuntary matrix, then a. A-I=O b. A+I=O c. A-...

    Text Solution

    |

  9. if A and B are squares matrices such that A^(2006)=O and A B=A+B , the...

    Text Solution

    |

  10. If matrix A is given by A=|[6, 11], [2, 4]| , then the determinant o...

    Text Solution

    |

  11. If A=[(a, b, c), (x, y, z), (p, q, r)], B=[(q,-b, y),(-p, a,-x),(r,-c,...

    Text Solution

    |

  12. If A and B are two non-singular matrices such that A B=C ,t h e n,|B| ...

    Text Solution

    |

  13. If A(alpha,beta)=[cosalphas inalpha0-s inalphacosalpha0 0 0e^(beta)],t...

    Text Solution

    |

  14. If A=[[a+i b, c+i d],[-c+i d, a-i b]] and a^2+b^2+c^2+d^2=1,t h e n ...

    Text Solution

    |

  15. Statement 1: A=[(4,0,4),(2,2,2), (1,2,1)] B^(-1)=[(1,3,3),(1,4,3),(1,3...

    Text Solution

    |

  16. If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],...

    Text Solution

    |

  17. Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ...

    Text Solution

    |

  18. A 3xx3 matrix given as, a(i j)=(i-j)/(i+2j) cannot be expressed as a s...

    Text Solution

    |

  19. Statement 1: If A ,B ,C are matrices such that |A(3xx3)|=3,|B(3xx3)|=-...

    Text Solution

    |

  20. Statement 1: For a singular square matrix A ,A B=A C B=Cdot Statemen...

    Text Solution

    |