Thread: space vector

Check whether the data sets together with the operations indicated is a space vector. If not, list the properties that fail

1) V={(x,y,z)/x,y,z E R} , and

My Solution:

a) u+v=v+u
(x1,y1,z1)+(x2,y2,z2) = (x2,y1+y2,z2) = y1 + (x2,y2,z2) Not Check

b) u+(v+w) = (u+v)+w
...
= (x3,y1+y2+y3,z3) Not Check

c) u+e=u
I could not resolve

d) u+(u')=e
I could not resolve

e)
...
= Check

f)
...
= Not Check

g) 1 * u = u
...
= (x1,y1,z1) Check

h)
...
= Not Check



2) V={(x,y)/x,y E R} , and

a) Check
b) Check
c) Check
d) I could not resolve
e, f , g and h ) Not yet done


Thanks

There is no definition of the product of two elements in ?!
You put a product with a scalar and an element of , but not between elements of . Are you sure no information about the problem is missing?
Anyway, I didn't check all but for the 1) so is not a vector space.
(Detail: while ).

And about the 2), it seems to be a vector space but as you didn't define the product of two elements in V, we cannot affirm it.