How to Prove a Set is Closed Under Vector Addition

[@josedonadito]

Thank you, Mr. Scorcerer (lol). Greetings from Guatemala!

[@kristystrives6979]

Him: "I hope this is useful for someone in the world"
Me *in Australia*: "THANK YOUUU"

[@TheMathSorcerer]

awesome!!!!!!

[@RyanLBuchanan]

Thank you so much for that, oh wise One! That really did help out & I appreciate how succinct & down-to-earth your explanation was, my Friend! Cheers!

[@obnoxioussangheili3418]

Very helpful, and clearly explained. Thank you so much!

[@TheMathSorcerer]

you are welcome!

[@andyhype2546]

What a legend. You sir deserve a religion dedicated to your teachings. Mathematics is more of a cult.

[@user-iq5iu2tt2h]

What

[@HYDRALISK99]

Thank you so much for this clear explanation!

[@TheMathSorcerer]

you are welcome!!

[@FangSquared]

Are the x vector and y vectors always the same? If not, how did you get them?

[@FangSquared]

Could the y vector be any scalar of the x vector?

[@AnkitKumar-vu2iy]

Amazing Video sir, Great work !!

[@TheMathSorcerer]

Thank you!!

[@MrTtawesome]

Hmm, so given that S is instead the function x^2=y, this wouldn't be closed under addition due to the two resulting vector additions not being multiple of each other?

[@KeketsiFrancisSebapo]

please help me to show this , "Let A be an m × n matrix and u, v ∈ Rn. Prove that
(a) A(u + v) = Au + Av. (b) A(cu) = c(Au), for any scalar c."