Hw8 - Homework 8 questions PDF

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Homework 8 questions...

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Note: all computations for the exercises from Strang should be exact. That is, where you have square roots, they should stay as square roots, not decimals. Feel free to use Sage, but be sure to explain all your work. Exercises from Strang 33.

P. 229 1, 5, 91 , 12, 17-19, 28; P 242 4, 6, 10, 11, 15, 19, 20, 23, 24, 32,

Extra Problem Find a matrix Q1 that reflects the plane R2 in the line y = 3x. Find another matrix Q2 that reflects the plane in the line y = − 12 x. Find the product Q1 Q2 . Geometrically, what kind of orthogonal matrix is it? Write down exactly what it does to the plane. Explain why this must be true in terms of geometry2 .

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The points referred to are (0, 0), (1, 8), (3, 8), and (4, 20). Use Sage Cell to find the solution. Ignore the last part of the question. Instead, plot the points and the parabola, as well as the errors. 2 The full explanation in terms of exact angles is not straightforward, but see how far you can get!...