How can you have a basis through the spanning set theorem? I thought the spanning set...

How can you have a basis through the spanning set theorem? I thought the spanning set has to be linear independent? Doesn't the spanning set theorem say that the vectors in the set are linear dependent as you can them as a linear combination of each other? Am I overthinking this or am I getting this wrong?

**UPDATED

I think I have the answer to my question, we use the theorem to basically turn the set into a linearly independent set by getting rid of the vectors we can write a combination of, correct?

Expert Solution

Colby Messinger answered 2 years ago

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