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...Linear algebra ma spring instructor m chirilus bruckner matrix sum scalar multiple product powers inverse transpose properties of addition and scalings let a b c be matrices the same size r s scalars d ra rb e sa f multiplication if is n p are columns then ab j i ij in mj mn row column rule for nj an such that all sums products dened bc associative law ac left distributive ba ca right scaling ima ain identity peculiarities general it not true you cannot conclude either or k z times t given its has as rows so amatrix said to invertible there x xa ax where this called usually denoted by other words aa analogy with numbers note might always exist algorithm nding reduce augmented...