Home
Class 12
MATHS
Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and ...

Let `A=[[2,0,7] , [0,1,0], [1,-2,1]]` and `B=[[-x,14x,7x] , [0,1,0] , [x,-4x,-2x]]` are two matrices such that `AB=(AB)^(-1)` and `AB!=I` then `Tr((AB)+(AB)^2+(AB)^3+(AB)^4+(AB)^5+(AB)^6)=`

Text Solution

Verified by Experts

The correct Answer is:
`1//5`
We have
`AB=[(5x,0,0),(0,1,0),(0,10x-2,5x)]=[(1,0,0),(0,1,0),(0,0,1)]`
`implies x=1//5`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Single)|65 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.4|12 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

A and B be 3xx3 matrices such that AB+A=0 , then

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

If A=[[4,0],[1,2]] and B=[[1,3],[2,0]] then |adj AB| is :

If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I , then tr. (A^(2)+B^(2)) is equal to ________.

Show that AB+bar(AB) is always 1.

Let A=[[3x^2], [1], [6x]],B=[a,b,c] and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2x,(x+2)^2],[ 2x,(x+2)^2, 5x^2]] be three given matrices, where a ,b ,ca n dx in Rdot Given that tr(AB)=tr(C). If f(x)=a x^2+b x+c , then the value of f(1) is ______.

A=[(3, 0), (4, 5)], B=[(6, 3), (8, 5)], C=[(3, 6), (1, 1)] find the matrix D, such that CD-AB=0 .

Let A=[(1, 2), (1, 3)], B=[(4, 0), (1, 5)], C=[(2, 0), (1, 2)] show that A(BC)=(AB)C

CENGAGE-MATRICES-Exercise 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

    Text Solution

    |

  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

    Text Solution

    |

  3. If A=[{:(0,1,1),(1,0,1),(1,1,0):}] show that A^(-1)=(1)/(2)(A^(2)=3I)

    Text Solution

    |

  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

    Text Solution

    |

  5. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

    Text Solution

    |

  6. If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta,...

    Text Solution

    |

  7. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

    Text Solution

    |

  8. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

    Text Solution

    |

  9. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

    Text Solution

    |

  10. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

    Text Solution

    |

  11. If square matrix a is orthogonal, then prove that its inverse is also ...

    Text Solution

    |

  12. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

    Text Solution

    |

  13. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

    Text Solution

    |

  14. Using elementary transformation, find the inverse of the matrix A=[(a,...

    Text Solution

    |

  15. Show that the two matrices A, P^(-1) AP have the same characteristic r...

    Text Solution

    |

  16. Show that the characteristics roots of an idempotent matris are either...

    Text Solution

    |

  17. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

    Text Solution

    |