Proof Writing • Question ○ Let V be a vector space ○ Let x,y∈V such that {x,y} is independent ○ Prove that {2x+y,3x+2y} is independent • Proof ○ Let c_1,c_2∈R be arbitrary constant ○ c_1 (2x+y)+c_2 (3x+2y)=0 ○ (2c_1+3c_2 )x+(c_1+2c_2 )y=0 ○ Let {█(d_1=2c_1+3c_2@d_2=c_1+2c_2 )┤, d_1,d_2∈R ○ d_1 x+d_2 y=0 ○ Because {x,y} is independent ○ d_1=d_2=0 ○ {█(d_1=2c_1+3c_2=0@d_2=c_1+2c_2=0)┤⇒c_1=c_2=0 ○ Therefore {2x+y,3x+2y} is independent • Prompt ○ Exchange proofs with someone else. In a different color of pen or pencil, give them written feedback on their proof. ○ The main things to be looking for are: § Is the proof logically valid? § Is the proof understandable and clearly written? § Is the proof well-organized? ○ Here are some more questions it might be useful to ask (but don
