Lecture Notes 12
3
MATA33H3 Full Course Notes
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" + etl i;) size :(n - 1) ( n - 1) , & column j : = 1- 1) i ,j c- { 1,2 , Gnj . ahh let ai = matrix obtained by removing row i & column j det (a) = [ aijci; = hi , cil -1 aizcizt - . are nzaij matrices. There now we define cij = ij - cofactor of a. D= [ai;] gij the entry in the rawi finding de:-(a) using co - factors (a) row expansion : we select a single row i. T det (a) = [ aijcij = g. j. Eats:|; ; det (a) = [ aijcij = 9: column expansion : we select column j. 1 azj czj -1 - - - + gnjcnj. I 5: , / + (c) c- 1) = (1) c- 1) def def z , Det (d) is a unique real n j=\ (2) 1- 1: o j=l i= 1.
