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Let X be a vector space. Let || and || || be two norms on X. When are these norms said to be equivalent? Justify your answer. Let X = R³. For X = (X₁, X₂, X3). Let ||x|| = x₁ |+|x₂|+|X3| ||1x||² = √√√x₁ 1² + 1x₂ 1² +1x31² Show that ||-||and|||| are equivalent.

Let X be a vector space. Let || and || || be two norms on X. When are these norms said to be equivalent? Justify your answer. Let X = R³. For X = (X₁, X₂, X3). Let ||x|| = x₁ |+|x₂|+|X3| ||1x||² = √√√x₁ 1² + 1x₂ 1² +1x31² Show that ||-||and|||| are equivalent.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let X be a vector space. Let || -| and ||-|| be two norms on X. When are these norms said to be equivalent? Justify your answer. Let X = R³. For X = (X₁, X₂, X3). Let ||x|| ' = x₁ |+|x₂|+|X3| ||1x||² Show that = √1x₁ 1² + 1x₂ 1² + 1x3|² X1 and | || are equivalent.
Transcribed Image Text:Let X be a vector space. Let || -| and ||-|| be two norms on X. When are these norms said to be equivalent? Justify your answer. Let X = R³. For X = (X₁, X₂, X3). Let ||x|| ' = x₁ |+|x₂|+|X3| ||1x||² Show that = √1x₁ 1² + 1x₂ 1² + 1x3|² X1 and | || are equivalent.
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