Show that the set V = {(x,x, y): x, y € R} is a vector space with standard operations on R3. Al. x+y= y + x for any x
Posted: Tue Apr 26, 2022 5:38 pm
- Show That The Set V X X Y X Y R Is A Vector Space With Standard Operations On R3 Al X Y Y X For Any X 1 (6.28 KiB) Viewed 37 times
- Show That The Set V X X Y X Y R Is A Vector Space With Standard Operations On R3 Al X Y Y X For Any X 2 (34.77 KiB) Viewed 37 times
Al. x+y= y + x for any x and y in V. A2. (x + y) +2= x + (y +z) for any x, y, and z in V. A3. There exists an element 0 in V such that x +0= x for each x EV. A4. For each x eV, there exists an element -x in V such that x + (-x) = 0. A5. a(x + y) = ax + ay for each scalar a and any x and y in V. A6. (a + b)x = ax + Bx for any scalars a and B and any x € V. A7. (af)x = a(Bx) for any scalars a and B and any xe V. A8. 1 . X= x for all x E V. C1. If xe V and a is a scalar, then ax e V. C2. If x, y € V, then x + y = V.