Solution Found!

Prove Theorem 2.2 for the case that ft is infinite, that is, R(T) = spm({T(v):vft})

Chapter 2, Problem 33

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Prove Theorem 2.2 for the case that ft is infinite, that is, R(T) = spm({T(v):vft}).

Questions & Answers

QUESTION:

Prove Theorem 2.2 for the case that ft is infinite, that is, R(T) = spm({T(v):vft}).

ANSWER:

Step 1 of 2

Suppose V and W be vector spaces and be linear.

Let  be a basis for V which is not finite.

To prove that .

Since is a basis for V, for each .

Again, being a subspace  contains .

Thus,

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back