Compute the following product.342-82-18-6-3-48-5 2-68-32-1-56-3

Answered: Image /qna-images/answer/8e6a94f6-4d1d-4f02-9a75-f3407a23aab5.jpg

Answered: 3 4 [: -8 -1 6 8 -6 -3 -4 8 -5 2 -6 8…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.1: The Geometry And Algebra Of Vectors

Problem 29EQ: Write out the addition and multiplication tables for 4.

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Write out the addition and multiplication tables for 4.
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You may have been surprised to read (in Thm. 2.12) that for any two integers there is going to be a greatest common divisor which can be written as a linear combination of the two values. In essence, what this says is that since the divisor divides both numbers, there is going to be some combination of multiples of the two that adds up to the divisor. For example, for the numbers 6 and 8, the greatest common divisor is 2 AND 2 = 3(6) + -2(8). Now, I could find that by looking at multiples until a find a combo that would add to 2. That would look like the following. 6 … 12, 18, 24, … 8 … 16, 24 What I would notice is that the 18 and 16 are 2 apart, which means I only need to use some positives and negatives for the coefficients. (This reminds me a lot of the hunt and peck form of factoring we sometimes teach students.) The power of this linear combination is that it gives us a way to write the divisor in terms of the original values we were given. That’s helpful. Which brings us to the…
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