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If matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)]...

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))`

A

100

B

50

C

200

D

None of these

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • If A = [ (-5,-8,0),(3,5,0),(1,2,-1)] then A is

    A
    idempotent
    B
    nilpotent
    C
    involutory
    D
    None
  • Let three matrices A = [(-1,3,2),(2,-1,3),(1,2,3)], B = , C = [(-2,2,-1),(3,-5,4),(5,-6,4)] The value of log_(sqrt(8/7))[Tr^(2)(A) + +Tr^(3) ((ABC)/(2))+ Tr^(3) ((A(BC)^(2))/(2))+Tr^(3) ((A(BC)^(2))/(2))+.....+ oo] is [Note : Tr. (P) denote trace of matrix P] and Tr^(3)(A) = (Tr(A))^(3)

    A
    `-4`
    B
    `2`
    C
    `6`
    D
    `4`
  • 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)

    A
    7
    B
    18
    C
    `-58`
    D
    `-1624`
  • Similar Questions

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    show that the matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is involutory.

    If A=[[-5,-8,0],[3,5,0],[1,2,-1]], then transpose of A is

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