Question

Vector space:
Let a and b be vectors.
Define addition a + b = (a1,a2) + (b1,b2) = (a1+b1+1,a2+b2+1)
and k(a) = (k*a1,k*a2)

Show that (-1,-1) is the zero vector.

Answer 1

The definition of zero vector (provided by my textbook) is that
0 + 0 = 0
and
k0 = 0 for all scalars k.

It is easy to show how 0 + 0 = 0
But assuming (-1,-1) is the zero vector, then
k0 = k(-1,-1) = (-k,-k) which does not equal the 0 vector??

Also I must show that a + (-a) = (-a) + a = 0
But a + (-a) = (1,1)

Answer 2

AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH!!!!!!. A.... A.... A PROOOOOOOOFFF