1.9. Consider the space R2 with the norm ||- ||p, introduced in Section [1.5 Forp = 1,2,00 draw the "unit ball" B, in the norm || ||pB₂ := {x € R² : ||x||p ≤ 1}.Can you guess what the balls Bp for other p look like? 1.5. Norm. Normed spaces. We have proved before that the norm ||v||satisfies the following properties:1. Homogeneity: ||av|| = |a|-||v|| for all vectors v and all scalars a.2. Triangle inequality: ||u+v|| ≤ ||u|| + ||v||.3. Non-negativity: ||v|| ≥0 for all vectors v.4. Non-degeneracy: ||v|| = 0 if and only if v = 0.Suppose in a vector space V we assigned to each vector v a number ||v||such that above properties 1-4 are satisfied. Then we say that the functionv → ||v|| is a norm. A vector space V equipped with a norm is called anormed space.

The vector space ℝ2 is equipped with the norm .p. The norm .p is defined as xp=x1p+x2p1p for p≥1,…

Answered: 1.9. Consider the space R² with the…

Advanced Engineering Mathematics

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Chapter2: Second-order Linear Odes

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1.9. Consider the space R² with the norm ||- ||p, introduced in Section [1.5 For p=1,2,∞o draw the "unit ball" B, in the norm ||- || B₂ := {x € R² : ||x|| p ≤ 1}. Can you guess what the balls B₂ for other p look like?