Question: Let F(R2, R2) denote the vector space consisting of all functions f: R2 R2. (a) Which of the following functions f(x, y) are elements? (i)

Let F(R2, R2) denote the vector space consisting of all functions f: R2 †’ R2.
(a) Which of the following functions f(x, y) are elements?
(i) x2 + y2
(ii)

(iii)

(iv)

(v)

(vi)

(b) Sum all of the elements of ,F(R2, R2) you identified in part (a). Then multiply your sum by the scalar -5.
(c) Carefully describe the zero element of the vector space .F(R2, R2).

cos y 3

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