Let V be the vector space of polynomials in t of degree ≤ 3. Determine whether the following vectors ⃗u, ⃗v, ⃗w are linear independent or dependent ? ⃗u = t3 − 3t2 + 5t + 1, ⃗v = t3 − t2 + 8t + 2, ⃗w = 2t3 + 4t2 + 9t + 5

Let V be the vector space of polynomials in t of degree ≤ 3. Determine whether the following vectors ⃗u, ⃗v, ⃗w are linear independent or dependent ? ⃗u = t3 − 3t2 + 5t + 1, ⃗v = t3 − t2 + 8t + 2, ⃗w = 2t3 + 4t2 + 9t + 5

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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Question

Let V be the vector space of polynomials in t of degree ≤ 3. Determine whether the
following vectors ⃗u, ⃗v, ⃗w are linear independent or dependent ?
⃗u = t3 − 3t2 + 5t + 1, ⃗v = t3 − t2 + 8t + 2, ⃗w = 2t3 + 4t2 + 9t + 5

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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