Prove that for any field F. GL(3, F)= F\{0}. Also provide an example toSL(3, F)support your proof.

Consider a map ϕ:GL3,F→F\0 defined by ϕA=det A for every matrix A. Then ϕAB=ϕAϕB, since determinant…

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Prove that for any field F, GL(3, F), SL(3, E = F\{0}. Also provide an example to support your proof.

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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Prove that for any field F. GL(3, F)
= F\{0}. Also provide an example to
SL(3, F)
support your proof.

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