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Exercise 3

Avg difficulty 2.5

Suppose that the matrix A=[131−215022]A = \left[\begin{array}{rrr} 1 & 3 & 1 \\ -2 & 1 & 5 \\ 0 & 2 & 2 \\ \end{array}\right] defines the matrix transformation T:R3→R3T:\real^3\to\real^3.

  1. Describe the vectors x\xvec that satisfy T(x)=0T(\xvec) = \zerovec.

  2. Describe the vectors x\xvec that satisfy T(x)=[−892]T(\xvec) = \threevec{-8}{9}{2}.

  3. Describe the vectors x\xvec that satisfy T(x)=[−82−4]T(\xvec) = \threevec{-8}{2}{-4}.

Austin, Understanding Linear Algebra, §2.5 Matrix transformations, Exercise 3

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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.