1. (a)Let||.||:R2 →[0,∞}bedefinedas||x||=|x1|+|x2|+|x1−x2|. Prove that ||.|| defined above is a norm on R2. (b) Using the norm defined in 1(a) above , find a positive number r, such that Br((2,1)) ⊆ B3((1,1)). (c) Using the norm defined in 1(a) above, find a positive number s, such that Bs((2, 1)) ∩ B3((3, 1)) ̸= ∅.

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1. (a)Let||.||:R2 →[0,∞}bedefinedas||x||=|x1|+|x2|+|x1−x2|. Prove that ||.|| defined above is a norm on R2.
(b) Using the norm defined in 1(a) above , find a positive number r, such that Br((2,1)) ⊆ B3((1,1)).
(c) Using the norm defined in 1(a) above, find a positive number s, such that Bs((2, 1)) ∩ B3((3, 1)) ̸= ∅.

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masud 2024-12-10T20:27:49+05:00 1 Answer 18 views Beginner
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  1. Mechanical Engineering Expert
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    2024-12-10T21:36:08+05:00
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