How do you find a basis for the given subspaces of and .
a. All vectors of the form (a,b,c), where a=0
b. All vectors of the form (a+b, a-b, b+c, -a+b)
c. All vectors of the form (a,b,c), where a-b+5c=0
I understand how you did this problem, but I am confused about your anser to part b:
Shouldn't this be (a,a,0,-a)+(0,-b,b,b)+(c,0,c,0)=a(1,1,0,-1)+b(0,-1,1,1)+c(1,0,1,0)
Set={(1,1,0,-1),(0,-1,1,1),(1,0,1,0)} for all vectors of the form (a+b, a-b, b+c, -a+b)? Thank you!
I understand how you did this problem, but I am confused about your anser to part b:
Shouldn't this be (a,a,0,-a)+(0,-b,b,b)+(c,0,c,0)=a(1,1,0,-1)+b(0,-1,1,1)+c(1,0,1,0)
Set={(1,1,0,-1),(0,-1,1,1),(1,0,1,0)} for all vectors of the form (a+b, a-b, b+c, -a+b)? Thank you!
Just add up the components together to see if they match up. Add up the first coordinate, second, third, and fourth. You should get which is what I get.
I apologize. You are correct but I made a mistake on the problem. The vectors were suppoed to be the form of (a+c,a-b,b+c,-a+b). I don't know why I didn't notice my typo. Thank you.