Matrices-calc project please please help?
any form of help is appreciated!
note: i dont know how to make matrices on computer so each of these is a 2 by 2 matrix...just in one set of brackets. numbers before comma are top row, after comma are bottom row
1. Consider matrix M= [2 0 , 0 2] calculate M^n for n= 2, 3, 4, 5, 10, 20, 50. Describe in workds any pattern observed. use pattern to find general expression for matrix M^n in terms of n
2. Consider matrices P=[3 1, 1 3] and S= [4 2, 2 4]
P^2=[3 1, 1 3]^2 =[10 6, 6 10] = 2[5 3, 3 5] ; S^2= same type of thing as P
Calculate P^n and S^n for other values of n and describe any observed patterns
3. Consider [k+1 k-1, k-1 k+1]
steps 1 and 2 contain examples of these matrices for k=1, 2, and 3. consider other values of k and describe any patterns you observe. generalize these results in terms of k and n
4. use technology to investigate what happens when further values of k & n. state scope of limitations of k and n
2007-10-14
00:59:11
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6 answers
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asked by
suryakant p
1