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Exercise 7

Avg difficulty 2.5

Suppose we have the vectors v1=[23−1], v2=[−124], w1=[3−110], w2=[−2401]\vvec_1 = \threevec{2}{3}{-1},~ \vvec_2 = \threevec{-1}{2}{4},~ \wvec_1 = \fourvec{3}{-1}{1}{0},~ \wvec_2 = \fourvec{-2}{4}{0}{1} and that AA is a matrix such that Col(A)=Span{v1,v2}\col(A)=\laspan{\vvec_1,\vvec_2} and Nul(A)=Span{w1,w2}\nul(A) = \laspan{\wvec_1,\wvec_2}.

  1. What are the dimensions of AA?

  2. Find such a matrix AA.

Austin, Understanding Linear Algebra, §3.5 Subspaces, 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.