Let V be a vector space over F and w₁, W2, W3 € V. Suppose the list w₁, W2, W3 is linearly independent. Show that the list W1, W2, W1 + 2w2+W3 is linearly independent.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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4.
Let V be a vector space over F and w₁, W2, W3 € V. Suppose
the list w₁, W2, W3 is linearly independent. Show that the list
W₁, W2, W₁ + 2W₂ + W3
is linearly independent.
Transcribed Image Text:4. Let V be a vector space over F and w₁, W2, W3 € V. Suppose the list w₁, W2, W3 is linearly independent. Show that the list W₁, W2, W₁ + 2W₂ + W3 is linearly independent.
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