Linear algebra The problems are posted below for your conven

The problems are posted below for your convenience. Let H be the set of points inside and on the unit circle in the xy-plane. That is, let H = {[x y]: x^2 + y^2 lessthanorequalto 1}. Find a specific example, two vectors or a vector and a scalar, to show that H is not a subspace of R^2.

Solution

x=[1 0]^T is one vector in H

because 1^1+0^1=1

So, x is on the circle

Let scalar be ,c=2

cx=[2 0]^T

2^2+0=4

So, cx is outside the circle hence not in H

HEnce, H is not closed under scalar multiplication and hence not a subspace