Science:Math Exam Resources/Courses/MATH307/April 2010/Question 04 (a)
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Question 04 (a)
Consider the following recursion relation:
where , and
Find the matrix so that for all n, we have
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Science:Math Exam Resources/Courses/MATH307/April 2010/Question 04 (a)/Hint 1
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It’s relatively simple to find the matrix we want. Using the relation given above and the knowledge that , we can see that the relation can be defined by the matrix equation:
but we want to define the term by a combination of and by having a matrix
We know what is,
So let’s use that knowledge and continue:
and when =
but we know what is, it’s merely
continuing along the trend above, we can see that, in general,