SOLUTION: This is the questions i'm sorry i cannot upload it http://i67.tinypic.com/i39lqq.png I found that a = 1/sqrt(2) but I have problem on 2nd and 3rd questions. How can I find s

Algebra ->  Matrices-and-determiminant -> SOLUTION: This is the questions i'm sorry i cannot upload it http://i67.tinypic.com/i39lqq.png I found that a = 1/sqrt(2) but I have problem on 2nd and 3rd questions. How can I find s      Log On


   



Question 1107053: This is the questions
i'm sorry i cannot upload it http://i67.tinypic.com/i39lqq.png
I found that a = 1/sqrt(2)
but I have problem on 2nd and 3rd questions. How can I find such n that change the matrix that way?

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
2.  Answer.  n = 6.

    You can easily check it directly on your own:  A%5E6 = -I%2AA%5E2 = %28matrix%282%2C2%2C+0%2C1%2C+-1%2C0%29%29.



3.  You have  A%5E4 = -I.

    Then A%5E8 = I.

    It means that every 8-th degree of A will be equal to I.


    It also means that the sequence of i-th degrees is cyclical/periodical with the period of 8:

    n        1    2    3    4    5    6    7    8    9    10

   A%5En:      A   A%5E2   A%5E3  -I   -A  -A%5E2  -A%5E3   I    A    A%5E2  . . . periodical with the period 8 . . . 

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With this HINT, can you complete the assignment ?