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Suppose T: R² → R2 is the linear transformation defined in the figure below. The figure shows where T maps 8 vectors V₁,..., vg from the domain. With this limited information about T, what properties of T can be determined? У У -1 -2 -3 -4 v6 8 7 6 5 v4 4 3 2 1 v5 * v1 v3 v2 8 7 6 5 4 3 21 T(v2) T(v3) T(v4) T * T(v1) -1 -2 T(v8) T(v7) T(v6) -3 T(v5) x v7 v8 -5 -5 -6 -6 -7 -7 -8 -8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 domain codomain a. Select all the statements below that describe eigenvectors for the linear transformation T. There may be more than one correct answer. ☐ ☐ ☐ 00 ☐ ☐ ☐ ☐ ☐ A. B. e1- C. 30e2 [4.5] D. any nonzero vector parallel to the line y = x E. F. G. 0 450 H H. any nonzero vector parallel to the x-axis I. any nonzero vector parallel to the line y = -x J. any nonzero vector parallel to the line x = 0 b. The set of all eigenvectors of the linear transformation T with eigenvalue -1.5 together with the zero vector 0 is the eigenspace E-1.5. When described in words, th set E-1.5 is (select all that apply): ☐ ☐ ☐ ☐ ☐ A. the zero vector together with all vectors parallel to the y-axis B. the zero vector together with all vectors parallel to the line y = -x C. the zero vector together with all vectors parallel to D. the zero vector together with all vectors parallel to E. the zero vector together with all vectors parallel to F. the zero vector together with all vectors parallel to the x-axis c. The set of all eigenvectors of the linear transformation T with eigenvalue 0.5 together with the zero vector 0 is the eigenspace E0.5. When described in set notation, the set E0.5 is (select all that apply): ☐ PA. B. {k | | | | | k = R } {k [1 ] | k = R} C. {k | | | | k = R} D. {k [11] | k ≤ R}

Suppose T: R² → R2 is the linear transformation defined in the figure below. The figure shows where T maps 8 vectors V₁,..., vg from the domain. With this limited information about T, what properties of T can be determined? У У -1 -2 -3 -4 v6 8 7 6 5 v4 4 3 2 1 v5 * v1 v3 v2 8 7 6 5 4 3 21 T(v2) T(v3) T(v4) T * T(v1) -1 -2 T(v8) T(v7) T(v6) -3 T(v5) x v7 v8 -5 -5 -6 -6 -7 -7 -8 -8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 domain codomain a. Select all the statements below that describe eigenvectors for the linear transformation T. There may be more than one correct answer. ☐ ☐ ☐ 00 ☐ ☐ ☐ ☐ ☐ A. B. e1- C. 30e2 [4.5] D. any nonzero vector parallel to the line y = x E. F. G. 0 450 H H. any nonzero vector parallel to the x-axis I. any nonzero vector parallel to the line y = -x J. any nonzero vector parallel to the line x = 0 b. The set of all eigenvectors of the linear transformation T with eigenvalue -1.5 together with the zero vector 0 is the eigenspace E-1.5. When described in words, th set E-1.5 is (select all that apply): ☐ ☐ ☐ ☐ ☐ A. the zero vector together with all vectors parallel to the y-axis B. the zero vector together with all vectors parallel to the line y = -x C. the zero vector together with all vectors parallel to D. the zero vector together with all vectors parallel to E. the zero vector together with all vectors parallel to F. the zero vector together with all vectors parallel to the x-axis c. The set of all eigenvectors of the linear transformation T with eigenvalue 0.5 together with the zero vector 0 is the eigenspace E0.5. When described in set notation, the set E0.5 is (select all that apply): ☐ PA. B. {k | | | | | k = R } {k [1 ] | k = R} C. {k | | | | k = R} D. {k [11] | k ≤ R}

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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Suppose T: R² → R2 is the linear transformation defined in the figure below. The figure shows where T maps 8 vectors V₁,..., vg from the domain. With this limited information about T, what properties of T can be determined? У У -1 -2 -3 -4 v6 8 7 6 5 v4 4 3 2 1 v5 * v1 v3 v2 8 7 6 5 4 3 21 T(v2) T(v3) T(v4) T * T(v1) -1 -2 T(v8) T(v7) T(v6) -3 T(v5) x v7 v8 -5 -5 -6 -6 -7 -7 -8 -8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 domain codomain
Transcribed Image Text:Suppose T: R² → R2 is the linear transformation defined in the figure below. The figure shows where T maps 8 vectors V₁,..., vg from the domain. With this limited information about T, what properties of T can be determined? У У -1 -2 -3 -4 v6 8 7 6 5 v4 4 3 2 1 v5 * v1 v3 v2 8 7 6 5 4 3 21 T(v2) T(v3) T(v4) T * T(v1) -1 -2 T(v8) T(v7) T(v6) -3 T(v5) x v7 v8 -5 -5 -6 -6 -7 -7 -8 -8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 domain codomain
a. Select all the statements below that describe eigenvectors for the linear transformation T. There may be more than one correct answer. ☐ ☐ ☐ 00 ☐ ☐ ☐ ☐ ☐ A. B. e1- C. 30e2 [4.5] D. any nonzero vector parallel to the line y = x E. F. G. 0 450 H H. any nonzero vector parallel to the x-axis I. any nonzero vector parallel to the line y = -x J. any nonzero vector parallel to the line x = 0 b. The set of all eigenvectors of the linear transformation T with eigenvalue -1.5 together with the zero vector 0 is the eigenspace E-1.5. When described in words, th set E-1.5 is (select all that apply): ☐ ☐ ☐ ☐ ☐ A. the zero vector together with all vectors parallel to the y-axis B. the zero vector together with all vectors parallel to the line y = -x C. the zero vector together with all vectors parallel to D. the zero vector together with all vectors parallel to E. the zero vector together with all vectors parallel to F. the zero vector together with all vectors parallel to the x-axis c. The set of all eigenvectors of the linear transformation T with eigenvalue 0.5 together with the zero vector 0 is the eigenspace E0.5. When described in set notation, the set E0.5 is (select all that apply): ☐ PA. B. {k | | | | | k = R } {k [1 ] | k = R} C. {k | | | | k = R} D. {k [11] | k ≤ R}
Transcribed Image Text:a. Select all the statements below that describe eigenvectors for the linear transformation T. There may be more than one correct answer. ☐ ☐ ☐ 00 ☐ ☐ ☐ ☐ ☐ A. B. e1- C. 30e2 [4.5] D. any nonzero vector parallel to the line y = x E. F. G. 0 450 H H. any nonzero vector parallel to the x-axis I. any nonzero vector parallel to the line y = -x J. any nonzero vector parallel to the line x = 0 b. The set of all eigenvectors of the linear transformation T with eigenvalue -1.5 together with the zero vector 0 is the eigenspace E-1.5. When described in words, th set E-1.5 is (select all that apply): ☐ ☐ ☐ ☐ ☐ A. the zero vector together with all vectors parallel to the y-axis B. the zero vector together with all vectors parallel to the line y = -x C. the zero vector together with all vectors parallel to D. the zero vector together with all vectors parallel to E. the zero vector together with all vectors parallel to F. the zero vector together with all vectors parallel to the x-axis c. The set of all eigenvectors of the linear transformation T with eigenvalue 0.5 together with the zero vector 0 is the eigenspace E0.5. When described in set notation, the set E0.5 is (select all that apply): ☐ PA. B. {k | | | | | k = R } {k [1 ] | k = R} C. {k | | | | k = R} D. {k [11] | k ≤ R}
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