given that n (is a member) of +integers, x is a member of REal numbers, and M= cosh^2 x cosh^2 x
sinh^2 x sinh^2 x (2x2 matrix)
use induction to show that M^n=M
I can show that M^2=m but not sure how to use the let n=k method!
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ogs
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- 28-06-2004 18:58
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Juwel
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- 28-06-2004 19:01
(Original post by ogs)
given that n (is a member) of +integers, x is a member of REal numbers, and M= cosh^2 x cosh^2 x
sinh^2 x sinh^2 x (2x2 matrix)
use induction to show that M^n=M
I can show that M^2=m but not sure how to use the let n=k method! -
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- 28-06-2004 19:03
M^3
= M^2 M
= M^2 . . . because M^2 = M
= M . . . again because M^2 = M
M^4
= M^3 M
= M^2 . . . because M^3 = M
= M . . . because M^2 = M
M^5
= M^4 M
= M^2 . . . because M^4 = M
= M . . . because M^2 = M -
ogs
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- 28-06-2004 19:07
that won't work as a proof by induction though! as you have to consider a general value...
or will it? do you think that it would get the marks? -
It'sPhil...
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- 28-06-2004 20:08
(Original post by ogs)
that won't work as a proof by induction though! as you have to consider a general value...
or will it? do you think that it would get the marks? -
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- 28-06-2004 20:19
Here is a more formal presentation of the inductive step. Suppose that k >= 2 is an integer and M^k = M. Then
M^(k + 1)
= M^k M
= M^2 . . . because M^k = M
= M . . . proved in the first part of the question
So M^(k + 1) = M.
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