Determine whether the set, together with the indicated operations, is a vector s

Question

Determine whether the set, together with the indicated operations, is a vector space. If it is not, identify at least one of the ten axioms that fails. The set of all quadratic functions whose graphs pass through the origin with the standard operations. The set {(x,y): x 0,y e R} with the standard operations in R2. The set {(x;1/2 x): x e R} with the standard operations. The set of all 2 Times 2 diagonal matrices with the standard operations. A and B are row equivalent. Find bases for the row(A), col(A), and nul(A).

Explanation / Answer

(a)Vector space

(b)

(1,1) belongs to the set

but -1*(1,1) = (-1,-1) doesnt belong to the set

=>

NOT a vector space

(c)

Vector space

(d)

Vector space

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