MATH 136- Final Exam Guide - Comprehensive Notes for the exam ( 30 pages long!)
29 Mar 2018
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MATH136 Full Course Notes
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Friday, may 12 lecture 6 : dot products and norms (section 1. 4: algebraic properties of dot product of two vectors. 2 vectors x and y in n : x = (x1, x2, , xn) What we start with : and y = ( y1, y2, ,yn). 1 number x y in : x y = x1y1 + x2 y2 + + xn yn. Other notation for dot-product: x y = < x, y > 6. 1. 1 examples if x = (2, 1, 7) and y = (3, 9, 0) verify that x y = 3. 6. 1. 2 theorem algebraic properties of dot product. Suppose x, y and z are in n and in . Dp2 x y = y x. Dp3 ( x) y = (x y) Dp4 x (y + z) = x y + x z. Proofs are straightforward and are left as an exercise.
