Problem 13 1 Point Suppose T R R2 Is The Linear Transformation Shown In The Figure Below A The Vector V Corre 1 (78.11 KiB) Viewed 39 times
Problem 13. (1 point) Suppose T : R² → R2 is the linear transformation shown in the figure below. a. The vector v₁ corresponds to the eigenvalue b. The vector v₂ corresponds to the eigenvalue c. The vector V3 corresponds to the eigenvalue d. The vector v₁ corresponds to the eigenvalue e. The vector vs corresponds to the eigenvalue f. The vector V6 corresponds to the eigenvalue g. The vector V, corresponds to the eigenvalue 8 7 6 h. The vector vs corresponds to the eigenvalue 5 4 3 2 1 -1 -3 -8 vid v3 * V5 vi v7 v6 y -8-7-6-5-4-3 -2 -1 VB 1 2 3 4 5 6 7 8 x 8 7 6 For each of the following vectors, if the vector is an eigenvector for T, determine the corresponding eigenvalue. If the vector is not an eigenvector for T, enter NONE. A 4 3 1 T(v2) T(v1) -1 -2 -3 -4 -5 -6 -7 -8 -8 -7 -6 -5 -4 -3 -2 -1 T(V8) Ч T(v3) +7 T(97) T(4) T(5) T(V6) 1 2 3 4 5 6 7 8
Which of the following vectors are eigenvectors for the linear transformation T? Select all correct answers. □ A. (-1,-1) B. (0, -4) □c. (0,0) ☐ D. (9,0) E. (-8, 8) Which of the following sets is a basis for the eigenspace E0.5 of T? ○ A. {(1, 1)} ○ B. {(1,0)} ○ C. {(-1, 1)} D. {(0, 1)} Which of the following sets is a basis for the eigenspace E_₁ of T? A. {(0, 1)} B. {(-1, 1)} ○ C. {(1,0)} ○ D. {(1, 1)}
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