Mumbai University > Electronics and Telecommunication > Sem 4 > Applied Maths 4

Marks: 4M

Year: Dec 2014

A subset W of a vector space V is called subspace of V if W is itself a vector space under the addition and scalar multiplication defined in V, We need only to verify the axioms of closure (1) under addition & (2) scalar multiplication.

a) Closure:

$C_{1}$: If u = (1,x), v = (1,y) are two elements then

u + v = (1,x) + (1,y) = (1, x+y)

$\therefore$ W is closed under addition.

$C_{2}$: If u = (1,x) then

ku = k(1,x) = (1,kx)

$\therefore$ W is closed under multiplication.

Since W is closed under addition and scalar multiplication, W is a subspace of $R^2$.