- #1
Jaglowsd
- 7
- 0
Good evening everyone, I hope everyone is having a better evening than myself thanks to this homework problem.
Let P be the set of positive numbers. For a,b in P, define a+b=a x b; for a in P and a real number r, define r x a= a^r. Show that P is a vector space using ⊕ as addition and (circle dot) as scalar multiplication.
For a,b in P, define a⊕b=a x b; for a in P and a real number r, define r x a= a^r.
My professor wants us to use these properties that are in our text,
Properties:
1. X+Y=Y+X.
2. (X+Y)+Z=X+(Y+Z).
3. 0+X=X+0=X.
4. r(sX)=(rs)X.
5. (r+s)X=rX+sX.
6. r(X+Y)=rX+rY.
7. 1X=X.
My professor introduced our class to the topic of a vector space today and when he was talking about it everything made sense. Now that I am here on my own I honestly do not know where to start. Unfortunately I was unable to go to his office hours today to ask him about it.
A brief and general description of where I should start is all I ask.
Let P be the set of positive numbers. For a,b in P, define a+b=a x b; for a in P and a real number r, define r x a= a^r. Show that P is a vector space using ⊕ as addition and (circle dot) as scalar multiplication.
For a,b in P, define a⊕b=a x b; for a in P and a real number r, define r x a= a^r.
My professor wants us to use these properties that are in our text,
Properties:
1. X+Y=Y+X.
2. (X+Y)+Z=X+(Y+Z).
3. 0+X=X+0=X.
4. r(sX)=(rs)X.
5. (r+s)X=rX+sX.
6. r(X+Y)=rX+rY.
7. 1X=X.
My professor introduced our class to the topic of a vector space today and when he was talking about it everything made sense. Now that I am here on my own I honestly do not know where to start. Unfortunately I was unable to go to his office hours today to ask him about it.
A brief and general description of where I should start is all I ask.