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3320hw3

3320hw3 - Math 3320 Problem Set 3 1 1 This exercise is...

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Unformatted text preview: Math 3320 Problem Set 3 1 1. This exercise is intended to illustrate the proof of the Theorem on page 15 of Chapter 1 in the concrete case of the continued fraction 1 upslope ր 2 + 1 upslope ր 3 + 1 upslope ր 4 + 1 upslope ր 5 . (a) Write down the product A 1 A 2 A 3 A 4 = parenleftBigg 1 1 a 1 parenrightBiggparenleftBigg 1 1 a 2 parenrightBiggparenleftBigg 1 1 a 3 parenrightBiggparenleftBigg 1 1 a 4 parenrightBigg as- sociated to 1 upslope ր 2 + 1 upslope ր 3 + 1 upslope ր 4 + 1 upslope ր 5 . (b) Compute the four matrices A 1 , A 1 A 2 , A 1 A 2 A 3 , A 1 A 2 A 3 A 4 and relate these to the edges of the zigzag path in the strip of triangles for 1 upslope ր 2 + 1 upslope ր 3 + 1 upslope ր 4 + 1 upslope ր 5 . (c) Compute the four matrices A 4 , A 3 A 4 , A 2 A 3 A 4 , A 1 A 2 A 3 A 4 and relate these to the successive fractions that one gets when one computes the value of 1 upslope ր 2 + 1 upslope ր 3 + 1 upslope ր 4 + 1 upslope ր 5 , namely 1 upslope ր 5 , 1 upslope ր...
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