Let V = M3×3 (R) be the set of all 3 × 3-matrices. You can accept without proof that V is a vector space. Let H be the set of all 3 × 3 matrices with the property that A = -At. (The transpose A¹ is defined on page 109.) (a) Write down three different elements in H. (b) Explain why H is a subspace of V. (c) Find a basis for H.

Let V = M3×3 (R) be the set of all 3 × 3-matrices. You can accept without proof that V is a vector space. Let H be the set of all 3 × 3 matrices with the property that A = -At. (The transpose A¹ is defined on page 109.) (a) Write down three different elements in H. (b) Explain why H is a subspace of V. (c) Find a basis for H.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...

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