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Exercise 9

Avg difficulty 2.5

Suppose that kk is an unknown parameter and consider the set of vectors v1=[201],v2=[4−2−1],v3=[02k]\vvec_1 = \threevec{2}{0}{1}, \vvec_2 = \threevec{4}{-2}{-1}, \vvec_3 = \threevec{0}{2}{k}.

  1. For what values of kk is the set of vectors linearly dependent?

  2. For what values of kk does the set of vectors span R3\real^3?

Austin, Understanding Linear Algebra, §2.4 Linear independence, Exercise 9

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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.