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11. For what values of c are the vectors [-10 -1, 12 1 2], and (1 1 cl in Ra linearly dependent? 12. Suppose that S (V,Vz, Va) is a linearly independent set of vectors in a vector space V. Prove that T = (w,w2, Ws) is also linearly independent, where w = v + V2 + V3, Wz = vz + V3, and Wy = Vy. "

11. For what values of c are the vectors [-10 -1, 12 1 2], and (1 1 cl in Ra linearly dependent? 12. Suppose that S (V,Vz, Va) is a linearly independent set of vectors in a vector space V. Prove that T = (w,w2, Ws) is also linearly independent, where w = v + V2 + V3, Wz = vz + V3, and Wy = Vy. "

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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11 and 12 HANDWRITTEN
11. For what values of c are the vectors |-1o -1, 12 1 2), and [1 1 in Ry linearly dependent? 12. Suppose that S = (v,Vz, V3) is a linearly independent set of vectors in a vector space V. Prove that T = (W, w2, Ws) is also linearly independent, where w = vị + V2 + V3, Wz = vz + V3, and Ws = Vy.
Transcribed Image Text:11. For what values of c are the vectors |-1o -1, 12 1 2), and [1 1 in Ry linearly dependent? 12. Suppose that S = (v,Vz, V3) is a linearly independent set of vectors in a vector space V. Prove that T = (W, w2, Ws) is also linearly independent, where w = vị + V2 + V3, Wz = vz + V3, and Ws = Vy.
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