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December 29th, 2015, 03:41 AM  #1 
Newbie Joined: Dec 2015 From: Karachi Posts: 2 Thanks: 0  Column Matrix Expansion
Ok guys I want to ask a question that if we open a matrix by column then should we rotate the minor ? example: 1 1 1  2 0 1  2 1 3  I expand from C2 12 1 0 +(1)1 1 = (62)(1+2) = 11 2 3 2 1 Now I expand from R1 1 0 1 12 1 +(1)2 0 = (0+1)(62)(20)= 1+8+2=11 1 3 2 3 2 1 Determinant is different for both expansions Now I make some difference Again taking C2 11 3 0 +(1)1 1 = (2+6)(21) =8+3= 11 2 2 1 2 This time I rotated the 3x3 matrix before writing 2x2 determinants down Now you can see that before rotating the answer with row expansion did not match but after rotating it is matching But this thing seems new to me because once before my teacher didn't tell me anything about this even when I passed XI grade, now I am repeating it in some other city and my teacher told me this new thing Question: Is the rotating method an official method or it doesn't even exist ? Last edited by Ogie; December 29th, 2015 at 03:43 AM. 
December 29th, 2015, 07:05 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894  Quote:
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December 29th, 2015, 10:56 AM  #3 
Newbie Joined: Dec 2015 From: Karachi Posts: 2 Thanks: 0 
Thank you You solved my problem But I still have a question, why was the determinant of 3x3 matrix same upon rotating the 2x2 determinant ? 
December 31st, 2015, 10:23 AM  #4  
Newbie Joined: Dec 2015 From: Connecticut Posts: 21 Thanks: 4 Math Focus: I love to hate all of them equally  Quote:
if A = ( a b ) , then detA = ad  bc ( c d ) Set B to be the counterclockwise rotation of A. B = ( b d ) detB = bc  ad = detA ( a c ) Because your original mistake only caused a switch of each term's sign, rotation of each term's minor matrix corrected the mistake by switching it back.  

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