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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 181 and (3, 4). Altogether, C : Ail C! _ —A2 1A—1/3 C” : A%,1A4:11/3 T213 (Twillr \VJ ZAJi/SC” =T2’3C’” ZAEECHH __A21A—1/3T23A8/23 Cm! _ _A2, 1A_ 11313314831433 Cava- =A33CH’H We could tweak Cm” furthermore (by row operations) to obtain a row-reduced echelon matrix, which is characterized by the properties that (a) each pivot entry equals 1, and (b) in each column containing a pivot entry, all other entries are 0. To achieve (a), we merely have to apply some row scaling operations. To achieve (b), we need to apply upward row additions, i.e., row operations Aflm with a < ’a; this way we can clear out the entries above each pivot. But if we allow ourselves column operations as well, then we can even end up with a matrix which has entries 1 in cells (1, 1), (2,2) , . . . , (k, k) for some k, and entries 0 in all other cells. (Think of it as a truncated identity matrix, except that it is rectangular.) | TODO 3.161. History: [GrcarlO] reference. ...
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