Thread: vector

Are the vectors
in F(-infinity,infinity) the space of all functions from R to R linearly dependent or linearly independent?

Been a while since I've done this, but if I recall (and it makes sense, given the terminology), if you can write one of the vectors as a linear combination of the other vectors, then they're not all linearly independent. If this assumption is incorrect, well, throw this post away.

Note that we can rewrite as .

That's certainly a combination of the others:

3 is simply half the "6" vector, and the other part is 1.5 times the cosine-squared vector.

So I vote that they are not linearly independent.

Originally Posted by 00hyvs45

Are the vectors
in F(-infinity,infinity) the space of all functions from R to R linearly dependent or linearly independent?

I have answered this question in http://www.mathhelpforum.com/math-he...ly+independent. You could have asked me if you didnt understand, rather than editing the post