Home
Class 12
MATHS
If A=[(3,-4),(1,-1)] then find tr. (A^(2...

If `A=[(3,-4),(1,-1)]` then find tr. `(A^(2012))`.

Text Solution

Verified by Experts

`A=[(3,-4),(1,-1)]=[(1,0),(0,1)]+[(2,-4),(1,-2)]=I+B`
Now, `B^(2)=[(2,-4),(1,-2)][(2,-4),(1,-2)]=[(0,0),(0,0)]=O`
`implies A^(2012)=(I+B)^(2012)`
`=I^(2012)+^(2012)C_(1)I^(2012) B+O+O+..." "( :' B^(2)=B^(3)=B^(4) ... O)`
`=I+2012 B`
`=[(1,0),(0,1)]+2012 [(2,-4),(1,-2)]`
`:.` Trace of `A^(2012)=2+2012 (2-2)`
`=2`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.1|5 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.2|6 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

If matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] then find tr(A)+tr(A^(2))+te(A^(3))+…+tr(A^(100))

If A=[{:(1,3),(4,1):}] , then find |3A'| .

If A = [(0,4,3),(1,-3,-3),(-1,4,4)] , then find A^(2) and hence find A^(-1)

Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)], then find tr(A)-tr(B).

If A=[(2,-1),(3,4)] find |(A^(-1))^(-1)|

Let A=[[1, 1,3], [5, 2,6],[-2,-1,-3]] . Find t r(A^(2012))

If A=[(1,2,3),(2,1,2),(2,2,3)]B=[(1,2,2),(-2,-1,-2),(2,2,3)] and C=[(-1,-2,-2),(2,1,2),(2,2,3)] then find the value of tr. (A+B^(T)+3C) .

If A=[(2, 1,-1),(3, 5,2),(1, 6, 1)] , then tr(Aadj(adjA)) is equal to (where, tr (P) denotes the trace of the matrix P i.e. the sum of all the diagonal elements of the matrix P and adj(P) denotes the adjoint of matrix P)

" If matrix "A=[[1,1,3],[1,3,-3],[-2,-4,-4]]" then find "A^(-1)

CENGAGE-MATRICES-Solved Examples And Exercises
  1. If A=[(3,-4),(1,-1)] then find tr. (A^(2012)).

    Text Solution

    |

  2. In which of the following type of matrix inverse does not exist always...

    Text Solution

    |

  3. If both A-1/2Ia n dA+1/2 are orthogonal matices, then (a)A is ortho...

    Text Solution

    |

  4. If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (...

    Text Solution

    |

  5. If P is an orthogonal matrix and Q=P A P^T an dx=P^T Q^1000 P then x^...

    Text Solution

    |

  6. If A is a nilpotent matrix of index 2, then for any positive integer n...

    Text Solution

    |

  7. If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B...

    Text Solution

    |

  8. If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. ...

    Text Solution

    |

  9. If A is an orthogonal matrix then A^(-1) equals A^T b. A c. A^2 d. non...

    Text Solution

    |

  10. If A^2=1, then the value of det(A-I) is (where A has order 3) 1 b. -1 ...

    Text Solution

    |

  11. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

    Text Solution

    |

  12. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

    Text Solution

    |

  13. If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an ident...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

    Text Solution

    |

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

    Text Solution

    |

  18. Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |