Whats the answer for these vector spaces questions :

Question

Q1:determine whether the set, together with the indicated operations. Is a vector space.If it is not,identify at least one of the ten vector space axioms that fails.

1.The set {(x,y): x ≥ 0, y is a real number} with the standard operations in R²

2.The set of all 2 x 2 matrices of the form:

⌈a b⌉

⌊c 1⌋

with the standard operations

Answer 1

The sets are not vector spaces because they are not closed under scalar multiplication.

For example: (2,0) is in set 1, but -1(2,0) is not in the set. If we multiply a matrix in set 2 by a scalar other than 1, then the resulting matrix is not in the set