need immediate help...vector proof x+y=x+z?

Question

proof that y=z

"subtract x from both sides"

i wish it was that easy.. it's supposed to be more detailed than that... thanks anyway

Answer 1

x+y=x+z so if we divide both side by x(to eliminate x) we get

y=z

Answer 2

Subtract x from both sides.
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O.K. Be x=(x1, x2 , ..., x(n))

y=(y1, y2, ..., y(n))

z=(z1, z2, ..., z(n))

x + y = (x1+y1, x2+y2, ..., x(n)+y(n))

x + z = (x1+z1, x2+z2, ..., x(n)+z(n))

Plug into x + y = x + z

(x1+y1, x2+y2, ..., x(n)+y(n)) = (x1+z1, x2+z2, ..., x(n)+z(n))



Now, for every natural k between 1 and n
x(k) + y(k) = x(k) + z(k)

Thus z(k)=y(k) for every natural k between 1 and n

Thus, y = z

Answer 3

x+y=x+z
y =x+z-x
y = z