- #1
agary12
- 15
- 0
Homework Statement
I'm in 11th grade and I've been given the following in a series of problems:
(2 0)
(0 2)
Calculate M^N for 1,2,3,4,5,10,20,50. Describe any patterns you observe. Generalize the pattern into an expression for the matrix M^n in terms of n.
Homework Equations
The Attempt at a Solution
(2 0)
(0 2)^2 =
(4 0)
(0 4)
(2 0)
(0 2)^3 =
(8 0)
(0 8)
(2 0)
(0 2)^4 =
(16 0)
(0 16)
((2 0)
(0 2)^5 =
(32 0)
(0 32)
(2 0)
(0 2)^10 =
(1024 0)
(0 1024)
(2 0)
(0 2)^20 =
(1048576 0)
(0 1048576)
It looks like to me that you can multiply the value in the prior matrix by 2 (for powers 1-5) to get the new value in the next one. For example:
(2 0) (16 0)
(0 2)^4 = (0 16) so multiply 16 by 2 and you have 32. You then know that the matrix to the power of 5 will look like this:
(32 0)
(0 32)
Can someone help me find a rule in terms of n for M^n?