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THE ALGEBRA OF 2x2 MATRICES
MATRICES AND LINEAR SYSTEMS
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2x2 matrices addition and multiplication addition and subtraction additive inverse angle associative Chapter coefficient column vectors commutative law complex numbers compute coordinates Corollary corresponding entries defined definition denote determine direction cosines elementary matrices elementary row operations equal equivalent example Exercises Figure function geometric vectors group under multiplication Hence i—th row identity matrix inner product isomorphic j-th column j—th left—hand factor length linear combination linear equations linear transformation located vector m x n matrix maps mathematics matrix equation matrix multiplication matrix of order multiplicative inverse multiply Equation number of columns number of rows number of tubes obtain Equation one—to—one ordinary algebra orthogonal parallel parallelogram plane proof properties rational numbers real numbers represented row and j-th row vector satisfied Show solution square matrix subset subspace subspace of H systems of linear transformation on H vector of order vector space zero matrix