1.1 - MATH 232 a. Course is about Linear Algebra b. Came...

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Unformatted text preview: MATH 232 a. Course is about Linear Algebra b. Came about through study of equations which are linear c. Has developed into a framework and set of tools which are basic and useful (1) to all of mathematics and (2) in many applications 1 1.1 Systems of Equations Some motivating examples: Generally, we consider equations involving vectors vectorx = x 1 . . . x p R p where R = real numbers, but for now simply consider p = 1 and the scalar equation 2 x = 3 for x R . Solve using the tools of arithmetic: If 2 x = 3 then 1 2 2 x = 1 2 3, so x = 3 2 This seems trivial, right? But what about x = 3 What can x be? x = 0 What can x be? Notice: We have examples where there is a unique solution , no solution , or infinitely many solutions SUMMARY: ax = b has unique soln ( x = b a if a negationslash = 0) no soln (if a = 0 , b negationslash = 0) infinitely many solns (if a = 0 , b = 0) 2 A more complicated example: Now take two variables x and y (so vectorx = bracketleftBigg x y bracketrightBigg ) E 1 2 x + y = 1 E 2 3 x 4 y = 3 manipulate one linear system to an...
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1.1 - MATH 232 a. Course is about Linear Algebra b. Came...

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