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Question Number 120524 by SOMEDAVONG last updated on 01/Nov/20

$$1/.\mathrm{Given}\mathrm{E}=\mathrm{C}([0,1],\mathbb{R})\mathrm{are}\mathrm{mapping}\mathrm{set}[0,1]\to \mathbb{R}.$$$$\left(\mathrm{a}\right).\mathrm{Show}\mathrm{that}\mathrm{E}\mathrm{is}\mathrm{vector}\mathrm{space}.$$$$\left(\mathrm{b}\right).\mathrm{For}\mathrm{f}\in \mathrm{E},\mathrm{let}\mid \mid \mathrm{f}\mid {\mid }_1={\int }_0^1\mid \mathrm{f}\left(\mathrm{x}\right)\mid \mathrm{dx}.$$$$\mathrm{Show}\mathrm{that}(\mathrm{E},\mid \mid .\mid {\mid }_1)\mathrm{are}\mathrm{normed}\mathrm{space}.$$$$\left(\mathrm{Helpe}\mathrm{me}\mathrm{please}\right)$$

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