MATH215 Lecture 10: note10

• School: University of Alberta
• Department: Mathematics
• Course: MATH215
• Professor: Alexander Litvak

Document Summary

Determinants: de nition of determinants let a = (aij)1 i,j n be an n n square matrix. For a 1 1 matrix a = (a), we de ne det a = a. For a 2 2 matrix a = (aij)1 i,j 2, we de ne det a = (cid:12)(cid:12)(cid:12)(cid:12) a11 a12 a21 a22(cid:12)(cid:12)(cid:12)(cid:12) The matrix obtained by deleting the ith row and jth column of a is called the ijth minor of a and is denoted by aij. The cofactor of the entry aij in a is de ned to be ( 1)i+j det aij. The determinant of a is given by det a = n. Xj=1 ( 1)i+jaij det aij expansion by ith row or det a = n. Xi=1 ( 1)i+jaij det aij expansion by jth column.