MATH 133 Lecture Notes - Laplace Expansion

• School: McGill University
• Department: Mathematics & Statistics (Sci)
• Course: MATH 133
• Professor: Djivede Kelome

Document Summary

We can view det (read determinant) as a function which uses a square matrix(ie a nxn matrix) as a input and the output is a real number denoted det(a) Let a be a nxn matrix let a. be the sub matrix of a obtained by deleting the ith row and the jth column of a. Since i and j can take any value from 1 to n there are n cofactors. We can therefore de ne a matrix such that its (i,j) entry is such matrix is called cofactor matrix (of a) we will donote it cof(a) Adjoint of a: given a a nxn matrix, the adjoint of a is the nxn matrix de ned as. Fix a row of a (let us say the ith row) the entries are ai1,ai2,,ain. Remark: it does not matter which row we use in the cofactor expansion, we can also do a cofactor expansion along a column.