Number 7

T : v -> v by definition :

If P (x,y) then :

i)                     T (P) = ( x+1,y) for x ≥ 0

ii)                    T (P) = ( x -1,y) for x < 0

Answer :

Is T injective ?

If A prapeta for point of A (x,y)

X + 1,y = x,y = y

X = x,y – 1,y

Y = y

For example A (x,y1) and B (x2, y2)

T (A) = (x1+1,y1) and T(B) = (x2-1, y2)

So x1 + 1 = x2 – x1 and y1 = y2, such that x1 = x2 and y1 = y2 so A = B

Is T transformation ?

If T injective and T is bijective domain. So that T is transformation from V to V.