Show that the set Fm×n of all m×n matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a matrix by a scalar as scalar multiplication.

Show that the set Fm×n of all m×n matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a matrix by a scalar as scalar multiplication.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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