Give an example where the statement: If U and V are vector subspaces of Rn, then U ∪ V is also a vector subspace of Rn. holds true. Note that this will hold true if U is a subset of V or vice versa. Kindly give an example for R2. I would prefer if the example is in matrix form.

Give an example where the statement: If U and V are vector subspaces of Rn, then U ∪ V is also a vector subspace of Rn. holds true. Note that this will hold true if U is a subset of V or vice versa. Kindly give an example for R2. I would prefer if the example is in matrix form.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...

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Question

Give an example where the statement:

If U and V are vector subspaces of Rⁿ, then U ∪ V is also a vector subspace of Rⁿ.

holds true.

Note that this will hold true if U is a subset of V or vice versa. Kindly give an example for R². I would prefer if the example is in matrix form.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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