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
Stacey Warren - Expert brainly.com
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make a matrix of the coefficient vectors|dw:1329543360004:dw|you have many methods to check for a linearly dependent set of vectors, but taking the determinant is probably easiest here
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right, is it zero here?
I got 5.
For question 2, does is make sense to divide f(3)/f(2)?
you 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
I don't see much sense in division
I see two ways to go about it; not sure which one you want
|dw:1329544485800:dw|1) 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^