combinepdf-min-0182.pdf

# combinepdf-min-0182.pdf - Notes on linear algebra(Monday...

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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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