**Unformatted text preview: **Notes on linear algebra (Monday 17th October, 2016, 23:10) page 29 with
P m
E 2 like
6:1 1:21 \_V_/
=H1a +ﬂza+* * ' +ﬂma
(by the deﬁnition of the 2 sign) P
= 2011,19“ ‘l— (12:3 ‘l— ' ' ' + 3mg?)
6:] = (31,1 -l- £12,] + ' ' ' +am,1) + ((112 + £12; + ' ' ' -|- 3mg) + ' ' ' -l- ((114; +1124; + ' ' ' + amp)
(by the deﬁnition of the 2 sign) 2 (the sum of all possible numbers akrg) ,. m P P m
WE obtain 2 ( E 3.393) = E ( ﬂkrg) .
k=1 3:1 6:1 k 1
(A more rigorous proof could be given using induction; but I don’t want to move to that level of formalism in these notes. Notice the visual meaning of the above
proof: If we place the mp numbers ﬂk’g into a matrix (am) then m P
o the number 2 Z ﬂkrg is obtained by summing the entries in each row of the L ‘1 I? 1 ...

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- Spring '13
- Greene
- Linear Algebra, Algebra