Verify that the following axiom holds or does not hold for t

Verify that the following axiom holds (or does not hold) for the vector space:

Axiom: If k is any scalar and u is any object in V, then ku is in V. Vector Space: A subspace of R2: the set of all length-2 vectors [x; y] such that x >=0 and y >=0. Note that this is just the 1st quadrant of the 2-D plane.

Solution

axiom doesnot hold as in given subspace

we have a restriction that x and y should be greater than equal to zero and

if we multiply by any scalar to a vector then the vector may or may not belong to the subspace because of the given restrictions.