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Back to The dot product

Exercise 7

Avg difficulty 2.5

Explain your responses to these questions.

  1. Suppose that v\vvec is orthogonal to both w1\wvec_1 and w2\wvec_2. Can you guarantee that v\vvec is also orthogonal to any linear combination c1w1+c2w2c_1\wvec_1+c_2\wvec_2?

  2. Suppose that v\vvec is orthogonal to itself. What can you say about v\vvec?

Austin, Understanding Linear Algebra, §6.1 The dot product, Exercise 7

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.