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. ...
View Full Document