MATH 1ZC3 Study Guide - Final Guide: Mexican Peso, Conjugate Transpose, Transpose
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A i o ehomogenous ofleading 1 s rank nullity n rank offreevariables. Homogenoussystem if rank n uniquesolution thetrivialsolution if rank n infinitelymanysolutions becausefreevariable a norate constant. Matrix multiplication dimensions mxn x n xp m xp. Trace addentries on the diagonal ka lareconstantsi a b c arematrices. Ab o doesn"timply a o or b 0. Elementary matrices resultfrom one row operation onthe i matrix. Solving linearsystems by matrixinversion is unique ab i eac i b c. L onto detlb d de ldn l is t l diagonalmatrix is invertible if alldiagonalenteries arenonzero det401. 6 if ais invertible aat andata arealsoinvertible s on diagonal arezero. Determinantformn nz3 a c t a cut ta nc n. Det b cdetca delca detai if n nmatrixahasonerowwhichis a scalar multipleofanotheroronecolumnwhich is ascalarmultipleof another delia o. A de"tca adja i usewhenaskedfora certainentry whendoingthiswillbeaskedforcisthentry lookataandusecjis entry. Geometricmalt ofparameters ofvectors hof0rowsinrref ofcti a detca a 1a hn matrix is invertibleaslongasno1 0 because7 detto.
