Re: Subspaces and functions

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Originally Posted by

**Tala** Which of the following 3 functions belong to W ? z_{1}(t) = 3e^{t}, z_{2}(t) = cos(t), z_{3}(t) = sinh(t)

We have , so the three funtions belong to .

Re: Subspaces and functions

Can you give an explanation ?

Re: Subspaces and functions

Quote:

Originally Posted by

**Tala** Can you give an explanation ?

Better ask your concrete doubts.

Re: Subspaces and functions

I don't understand how you get z2 to that form ?

Re: Subspaces and functions

Re: Subspaces and functions

This might be stupid but I don't get your z2 expression when I isolate cost in e^it = cost + i*sint ?

Re: Subspaces and functions

Quote:

Originally Posted by

**Tala** This might be stupid but I don't get your z2 expression when I isolate cost in e^it = cost + i*sint ?

Don't worry. We have

Now, sum and .

Re: Subspaces and functions

I see ! That makes sense.

And one last question the functions belong to W because they each can be written as a linear combination of span(e^{-t}, e^{-it}, e^{t}, e^{it}) right ?

Re: Subspaces and functions

Quote:

Originally Posted by

**Tala** I see ! That makes sense.

And one last question the functions belong to W because they each can be written as a linear combination of span(e^{-t}, e^{-it}, e^{t}, e^{it}) right ?

Well, as linear combination of those four functions.

Re: Subspaces and functions

Thank you for your help !

Re: Subspaces and functions

Quote:

Originally Posted by

**Tala** Thank you for your help !

You are welcome! :)