MATH 1ZC3 Lecture 5: 1.6 more on linear system
20 Feb 2019
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If it is nxn and invertible thenfor each b the system. A x b has exactly1solution x a l b prone at d. Letit be ni n phast. be ae andba i thenit is invertibleandb a t a if b ish. xu. If bismaandab i thenitisinvertible andb a t recall aisinvertibleisail ea icdefineinverse accordingtothe h if bisnxn thenad i provesba ingeneral abtba. Pref showa isinvertible supposethatxtis asolution to a le a xt o recall assume ba i b a l then. I ifakio hasonly trialsolution accordingto theteae equavilent theorem ais de invertible so ai ohasonlytrivialsolution thurible showthat a13 2 lasba i isassumed. Ab i so b a 1 counterexample if neither aandbare squarebut ab i itispossiblethat bail. Examplei findcaditionson bi bubs sothat. tkfollowingsystemis consistent recalltheorem is invertiblethenthesystem if wouldconsistent foreverychoiceofb if isnotinvertiblethesystemis onlyconsistentforsomechoiceofb. 2x 17113 5b l sulk by eliminationandseewhat barises additionaltheorem introducednextclass l f y bf to bb to 4 i.
