## 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

1. TuringTest

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

2. TuringTest

once you respond about that we'll discuss part 2

3. anonymous

So if the determinant = 0 it is dependent?

4. TuringTest

right, is it zero here?

5. anonymous

I got 5.

6. anonymous

For question 2, does is make sense to divide f(3)/f(2)?

7. TuringTest

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

8. TuringTest

I don't see much sense in division I see two ways to go about it; not sure which one you want

9. TuringTest

|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^

10. anonymous

Thanks. Got it