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