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...Chapter matrices daniel chan unsw term in this were rst introduced the chinese nine chapters on mathematical art to solve linear eqns mid s senior wrangler arthur cayley studied their own right and showed how they have an interesting useful algebra associated them wewill look at ideas extend vector arithmetic even show there is matrix multiplication akin multiplying numbers these will not only shed light solving also be later when you multivariable functions mappings some new notation for recall m n array of us scalars real or complex a mn weabbreviate above aij call ij th entry write wesay size because it has r resp c denote set all with entries sometimes abbreviate mmn if are understood irrelevant e g length column revise product let then x alternatively i note similarity dot products ainduces function t we our results but obvious analogues over complexes...