Let V = C² be the vector space over C and let a = {uj = (i, 1), uz = (1,0)} be vectors in V. Show that a forms a basis for V. Let W = M2x1(C) be a vector space over C. Give a basis ß for W. Let V and W be given as above. By using linear extension method, determine whether V is isomorphic to W for a and ß as basis in V and W, respectively. Find the matrix representation of the linear transformation in (c) with respect to the bases a and B of the vector spaces.

Let V = C² be the vector space over C and let a = {uj = (i, 1), uz = (1,0)} be vectors in V. Show that a forms a basis for V. Let W = M2x1(C) be a vector space over C. Give a basis ß for W. Let V and W be given as above. By using linear extension method, determine whether V is isomorphic to W for a and ß as basis in V and W, respectively. Find the matrix representation of the linear transformation in (c) with respect to the bases a and B of the vector spaces.

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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