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1. Is V a vector space? and Show that W is not a subspace

wow, okay. Thank you soo much chiro, you should be a college professor, if your not one already. You explain it very well. I'm glad I ran into you here, this whole physicsforum place is a very useful tool I didn't know existed. I'm definitely going to come back here more often, thanks again! :smile:
2. Is V a vector space? and Show that W is not a subspace

Okay, I see. You're right, I was using a lot of my intuition to prove the axioms (kinda funny how you knew my exact thought process). I guess I need to revisit the vector space chapter in the text. I'm using the anton 10th edition linear algebra book which I find not to be very concise. I need...
3. Is V a vector space? and Show that W is not a subspace

That makes perfect sense. I finished the problem, I am sure I am correct but again I need your counsel to reinforce my confidence for tomorrow's exam. I'm glad I did this on my own, otherwise I wouldn't have really understood this. Below are pictures of all my work, please let me know if I am...
4. Is V a vector space? and Show that W is not a subspace

Oh my gosh! I thought of the SAME EXACT THING!!! because a1 or b1 could be zeros (if it were within its domain). I do not know, the question does not state that, it only says: Let V be the set of all diagonal 2x2 matrices i.e. V = {[a 0; 0 b] | a, b are real numbers} with addition defined as...
5. Is V a vector space? and Show that W is not a subspace

Hmmm, I'm kind of stuck at axiom 4 (0+u=u+0=u). I believe it fails since adding a zero vector to u will result in a zero vector (as addition is defined to multiply). Please take a look at my work and tell me if I am correct. I am almost certain I am right but you guys are smarter than me :)...
6. Is V a vector space? and Show that W is not a subspace

thanks for the warm welcome and prompt reply chiro. I had to run to the market to get batteries for my calculator, but I have verified axiom 1 at least I think. I uploaded a picture of my work for axiom one, please let me know if I am correct or if I am wrong.
7. Is V a vector space? and Show that W is not a subspace

Hi all I hope you guys can help me. I am soo confused with this question: I would really liked a complete answer to this, I have an upcoming exam and I know these two will be on the exam. 1. Let V be the set of all diagonal 2x2 matrices i.e. V = {[a 0; 0 b] | a, b are real numbers} with...