Suppose T: R2 R² is the linear transformation defined in the figure below. The figure shows where T¹ maps 8 vectors V₁,..., ve from the domain. With this limited information about T, what properties of T can be determined? 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 V4 v5 v6 -6 -7 -8 -8 -7 -6 -5 -4 -3 -2 -1 y ▪ Eigenvectors: v3 v7 v2 domain 1 2 3 4 v8 v1 Part 1: Finding eigenvectors using geometry Which of the eight vectors drawn in the doma are eigenvectors? Enter your answer as a comma separated list of vector names, such a v1,v2. Part 2: Finding eigenvalues using geometry ☐ ļ ļ. 8 8 X T 8 7 6 5 4 3 2 1 T(2) T(v1) -1 -2 -3 -4 -5 -6 -7 -8 -8 -7 -6 -5 -4 -3 -2 -1 T(V8) y T(v3) T(47) T(V4) codomain T(5) X T(V6) 1 2 3 4 5 6 7 8

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