4. Prove the Triangle Inequality: If v, weV, then || v + w ||<|| v || + | w || -

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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4. Prove the Triangle Inequality: If v, weV, then || v + w ||<||v || + || w|| .
5. Let V be a vector space with a positive definite scalar product. Let v,...,v, be non-zero elements of V
which are mutually perpendicular, that is < v,v, >=0 if i + j. Show that they are linearly independent.
Transcribed Image Text:4. Prove the Triangle Inequality: If v, weV, then || v + w ||<||v || + || w|| . 5. Let V be a vector space with a positive definite scalar product. Let v,...,v, be non-zero elements of V which are mutually perpendicular, that is < v,v, >=0 if i + j. Show that they are linearly independent.
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