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
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
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86e98964-9a48-452e-bd4e-a22c8976527e%2Fcc91982e-837e-49ae-adff-ec5b2cb32421%2Fe231jpg_processed.jpeg&w=3840&q=75)
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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