Determine whether the following set equipped with the given operations is a vector space. If not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form (1,x) with the operations (1,y)+(1,y ′
)=(1,y+y ′
) and k(1,y)=(1,ky) (b) Determine whether the following set equipped with the given operations is a vector space. If not vector spaces identify the vector space axioms that fail. The set of all 2×2 matrices of the form [ a
0
​
0
b
​
] with the standard matrix addition and scalar multiplication.