Matrix Powers

... Table of contents: Questions: 1.) Consider the Matrix M= Calculate Mn for n= 2, 3, 4, 5, 10, 20, 50. Describe in words any pattern you observe. Use this pattern to find a general expression for the matrix Mn in terms of n. 2.) Consider the matrices P= and S= P2= 2 = =; S2= 2 = = Calculate Pn and Sn for other values of n and describe any pattern you observe. 3.) Now consider matrices of the form steps 1 and 2 contain examples of these matrices for K=1 2 and 3. Consider other values of k, and describe any pattern(s) you observe. Generalize these results in terms of K and N 4.) Use technology to investigate what happens with further values of k and n. State the scope or limitations of k and n. 5.) Explain why your results holds true in general. SL type 1: Matrix Powers 1) a) To calculate the value

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