Question

Show that u=yx-yz,v=x-2y-3z,w=x+2y-3z are dependent

Answer 1

Step-by-step explanation:

If

u ≡

x + y

x

and v ≡

x − y

y

,

then

u ≡ 1 +

x

y

and v ≡

x

y

− 1,

which gives

(u − 1)(v + 1) ≡

x

y

.

y

x

≡ 1.

Hence,

u ≡ 1 +

1

v + 1

and v ≡

1

u − 1

− 1.

2. If

u ≡ x + y and v ≡ x

2 + 2xy + y

2

,

then

v ≡ u

2

and u ≡ ±√

v.

If u and v are not connected by an identical relationship, they are said to be “independent

functions”.