- #1
agary12
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Homework Statement
In my other post I figured out that when
(2 0)
(0 2) = m
(2^n 0)
(0 2^n) = m^n
Now I have to find the determinate of each matrix M^N with powers from 1-5, 10 and 20.
Homework Equations
The Attempt at a Solution
det (M) is 4 which is also 2^2
det (M^2) is 16 which is also 2^4
det (M^3) is 64 which is also 2^6
det (M^4) is 256 which is also 2^8
det (M^5) is 1024 which is also 2^10
det (M^10) is 1048576 which is also 2^20
another way of writing this would be
det(M) the answer is 4 or 2^(2)
det(M^2) the answer is 16 or 2^(2+2)
det(M^3) the answer is 64 or 2^(2+4)
det(M^4) the answer is 256 or 2^(2+6)
det(M^5) the answer is 1024 or 2^(2+8)
det(M^10) the answer is 1048576 or 2^(2+18)
So basically it starts with det (M) being 4 and then each time you increase n by one the power of the answer goes up by two? How do I "generalize the pattern into an expression for det(M^n) in terms of n?