Let V = R³ be the vector space over R of dimension 3. (a) Let e1, e2, e3 be the standard basis vectors of R and set v4 = ej + e2 + €3. Show that the set of vectors {e1, e2, e3, v4} are linearly dependent. (b) Find a basis for the subspace U below – justify your answer. ai U = : а1, а2 € R (c) Define a function L : V →V by L: a2 a2 аз Show that L is a linear transformation.

Let V = R³ be the vector space over R of dimension 3. (a) Let e1, e2, e3 be the standard basis vectors of R and set v4 = ej + e2 + €3. Show that the set of vectors {e1, e2, e3, v4} are linearly dependent. (b) Find a basis for the subspace U below – justify your answer. ai U = : а1, а2 € R (c) Define a function L : V →V by L: a2 a2 аз Show that L is a linear transformation.

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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