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- Is the set S independent or dependent? Justify your answer. {(2,3, 1), (1,2, 1), (-2,3,3)} C R linearly %3D

- Is the set S independent or dependent? Justify your answer. {(2,3, 1), (1,2, 1), (-2,3,3)} C R linearly %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Is the set S {(2,3, 1), (1,2, 1), (-2, 3, 3)} C R linearly %3D independent or dependent? Justify your answer. 7. Prove that the set S = {(1,3, 2), (3, 1, 2), (0, 1,0)} spans R. 8. Find a basis for R that includes the vectors (1,0, 2) and (0, 1, 1). Justify your answer. 9. Show that the function T: R → R defined by T(x, y, z) = (x – z, 2x + y, 2y – 3r) is a lincar transformation. 10. Define the function T: R3 → R as 2 1 T(v) = Av = -3 2 0 1 0- 0-1 Find the image of T(-4,5,1) and the preimage of (-1,2, 2). 11. Find the eigenvalues and the corresponding eigenvectors of the 2 matrix A 3
Transcribed Image Text:6. Is the set S {(2,3, 1), (1,2, 1), (-2, 3, 3)} C R linearly %3D independent or dependent? Justify your answer. 7. Prove that the set S = {(1,3, 2), (3, 1, 2), (0, 1,0)} spans R. 8. Find a basis for R that includes the vectors (1,0, 2) and (0, 1, 1). Justify your answer. 9. Show that the function T: R → R defined by T(x, y, z) = (x – z, 2x + y, 2y – 3r) is a lincar transformation. 10. Define the function T: R3 → R as 2 1 T(v) = Av = -3 2 0 1 0- 0-1 Find the image of T(-4,5,1) and the preimage of (-1,2, 2). 11. Find the eigenvalues and the corresponding eigenvectors of the 2 matrix A 3
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