(a) Prove that the vector space of all 2 2 matrices is a four-dimensional vector space...

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(a) Prove that the vector space of all 2 × 2 matrices is a four-dimensional vector space by exhibiting a basis.
(b) Generalize your result and prove that the vector space Mm×m consisting of all m × n matrices has dimension mn.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 08:32 AM

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(a) Prove that the vector space of all 2 2 matrices is a four-dimensional vector space...

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a is a basis since we can uniquely write any aE 11 bE 12 ...View the full answer

Applied Linear Algebra

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