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Let V = C 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. (a) (b) Let W = M2x1(C) be a vector space over C. Give a basis ß for W. (c) 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. (d) Find the matrix representation of the linear transformation in (c) with respect to the bases a and ß of the vector spaces.

Let V = C 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. (a) (b) Let W = M2x1(C) be a vector space over C. Give a basis ß for W. (c) 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. (d) Find the matrix representation of the linear transformation in (c) with respect to the bases a and ß of the vector spaces.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 22EQ
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Question 2 Let V = C² be the vector space over C and let a = {u1 = (i, 1), u2 = (1,0)} be vectors in V. Show that a forms a basis for V. (a) %3D (b) Let W = M2x1(C) be a vector space over C. Give a basis B for W. (c) Let V and W be given as above. By using linear extension method, determine whether V is isomorphic W for a and B as basis in V and w, respectively. (d) Find the matrix representation of the linear transformation in (c) with respect to the bases a and ß of the vector spaces.
Transcribed Image Text:Question 2 Let V = C² be the vector space over C and let a = {u1 = (i, 1), u2 = (1,0)} be vectors in V. Show that a forms a basis for V. (a) %3D (b) Let W = M2x1(C) be a vector space over C. Give a basis B for W. (c) Let V and W be given as above. By using linear extension method, determine whether V is isomorphic W for a and B as basis in V and w, respectively. (d) Find the matrix representation of the linear transformation in (c) with respect to the bases a and ß of the vector spaces.
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