2 Question 2Let V = C² be the vector space over C and let a = {u1 = (i, 1), u2 = (1,0)} bevectors 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 B for W.(c)Let V and W be given as above. By using linear extension method, determinewhether 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 respectto the bases a and ß of the vector spaces.

Answered: Image /qna-images/answer/efb3674a-584a-49d9-b71c-de932a043858.jpg

Answered: Let W = M2x1(C) be a vector space over…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.1: Orthogonality In Rn

Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...

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Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
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Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..
In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem 5.2 to express was a linear combination of these basis vectors. Give the coordinate vector[w] ofwwith respect to the basis ={v1,v2}of 2or =v1,v2,v3 of3. v1=[111],v2=[110],v3=[112];w=[123]

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