m235notes1 - Notes 1: Some Applications of Linear Algebra...

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Unformatted text preview: Notes 1: Some Applications of Linear Algebra What is linear algebra? To begin with it has to do with equations of the form 3 x + 2 y = 1 (1)- x + 4 y = 7 , (2) that is, equations that do not involve products of variables or trig functions or exponentials or .... Thus x 2 + x sin y = 3 is not a linear equation. Linear equations are ubiquitous. Let me give an example. Consider an underwater vessel with three engines, each pointing in a different direction, each capable of pushing the vessel in one direction by an arbitrary strength. Notation : The symbol R stands for the real numbers, R 2 is the usual cartesian plane, that is, { ( x,y ) | x,y ∈ R } , and R 3 = { ( x,y,z ) | x,y,z ∈ R } is three space. We have R n = { ( x 1 ,x 2 ,... ) | x i ∈ R } . Let’s call our engines A,B,C and say that A,B,C produce motion in the directions A = 1 1 1 ,B = 1- 1 ,C = 1- 1 ....
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This note was uploaded on 11/22/2011 for the course MATH 235 taught by Professor Markman during the Fall '08 term at UMass (Amherst).

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m235notes1 - Notes 1: Some Applications of Linear Algebra...

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