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anonymous
 4 years ago
Are these set of functions linearly independent? If they are dependent, state the relation.
1. f1(x) = 2x − 3, f2(x) = x^2 + 1, f3(x) = 2x^2 − x
2.f1(x) = 2x − 3, f2(x) = 2x^2 + 1, f3(x) = 3x^2 + x
anonymous
 4 years ago
Are these set of functions linearly independent? If they are dependent, state the relation. 1. f1(x) = 2x − 3, f2(x) = x^2 + 1, f3(x) = 2x^2 − x 2.f1(x) = 2x − 3, f2(x) = 2x^2 + 1, f3(x) = 3x^2 + x

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2make a matrix of the coefficient vectorsdw:1329543360004:dwyou have many methods to check for a linearly dependent set of vectors, but taking the determinant is probably easiest here

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2once you respond about that we'll discuss part 2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So if the determinant = 0 it is dependent?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2right, is it zero here?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For question 2, does is make sense to divide f(3)/f(2)?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2you want to establish a relationship between them if they are not linearly dependent assuming you already figured out that they are not you want to see if you can make a formula from some linear combination of one or two vectors to produce the third

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2I don't see much sense in division I see two ways to go about it; not sure which one you want

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2dw:1329544485800:dw1) Use gaussian elimination and you will get at least one variable that takes on all real values 2) a little squinting and you may notice that\[\frac32f_2(x)+\frac12f_1(x)=f_3(x)\]I like this solution better^
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