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Lecture

# Detereminants

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University of Toronto Scarborough

Mathematics

MATA23H3

Sophie Chrysostomou

Winter

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Determinants Areas, Volumes and Cross Products Denition: (i) The determinant of 1 1 matrix is its sole entry. (ii)The determinant of a 2 2 matrix is given by a1 a2 a1 a2 det(A) = = a 1 2 b a 1 2 where A = b1 b2 b1 b2 (iii) The determinant of a 3 3 matrix is given by a1 a 2 a 3 det(A) = b1 b2 b 3 = a 1 b2 b3 a 2 b1 b3 + a 3 b1 b2 c2 c3 c1 c3 c1 c2 c1 c2 c 3 Denition: If a = [a ,a ,1 ],2 = 3b ,b ,b ] 1 R 2he 3ross product of a and b is given by # a b = a2 a3 , a 1 a 3 , a 1 a 2 = i a2 a 3 j a1 a 3 + k a 1 a2 b2 b3 b1 b 3 b1 b 2 b2 b3 b1 b3 b 1 b2 Note: a b is perpendicular to both a and b. 1 2011 by Sophie Chrysostomou www.notesolution.com

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