Problem 17SE

Show that it is impossible to find a basis for the vector space of n × n (n > 1) matrices such that each pair of elements in the basis commutes under multiplication.

1-20-17 Tuesday, September 6, 20111:06 AM Important Points • The Scientific Method ○ Observation, Representation, Interpretation ○ Representationis a model • Classification of Matter ○ Anything that occupies spaceand has mass. ○ Governed by two things: compositionand energy. ○ Mixtures: A combinationof two or more substancesin which the substancesretain their identities. Homogenous mixtures: compositionof the mixture is the samethroughout. Heterogenousmixtures: compositionis not uniform throughout Physical means can be used to seperatemixtures into its pure components ○ Substances:Compounds and elements. Elements cannot be seperatedinto simplersubstancesby chemical mean