C. Since C SNEN 2. Suppose that V and Ware vector spaces over F. Consider the cartesian product V x W, with vector addition and scalar multiplication defined by (V1.W)+(V2, W2) (V1+V2, W₁ + W₂) for every (V1, W1). (V2, W2) EV x W and e€ F. a) Show that V x W is a vector space over F. and (v, w) (cv,₁) b) Suppose that || ||v is a norm on V and || ||w is a norm on W. Show that (v, w) defines a norm on V x W. vy+ww

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