# Instructor's Guide for Poole's Linear Algebra - A Modern by Douglas Shaw, Michael Prophet

By Douglas Shaw, Michael Prophet

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Extra resources for Instructor's Guide for Poole's Linear Algebra - A Modern Introduction 2nd Edition

Example text

4 Beyond Parity We wish to transmit binary vectors of length 4 such as [1, 0, 1, 1] and [1, 1, 1, 0]. Because we are afraid of transmission error, we are going to add some bits to make an error-detecting code. Let v be the 4-bit vector we want to transmit. Bit number 5 will be v · [1, 1, 1, 1], bit number 6 will be v · [1, 1, 0, 0], and bit number 7 will be v · [0, 0, 1, 1]. All addition is modulo two. For example, [1, 1, 0, 1, 1] · [1, 1, 1, 1, 0] = 1. 1. If v = [1, 0, 1, 1], what vector will we transmit?

F (x) = 4x2 + 2x + 1 _2 _1 2.

Answer 1. Given at start of Problem 2 2. It is easy to solve; computations could have been made easier by dividing the equations at each stage to produce a leading coefficient of 1. 3. As above, the equations should be divided by their leading coefficients. 1 The Lemonade Trick A college student is dissatisfied with her lemonade options, and decides to mix three kinds of lemonade in her quest to find the perfect cup. ) and some of her grandmother’s watery lemonade (10% lemon juice, 10% sugar, 80% water, cherry juice, and a bit of Worcestershire sauce for “color”).