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Lecture

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McGill UniversityDepartment

Mathematics & Statistics (Sci)Course Code

MATH 133Professor

Djivede KelomeThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**Determinants

Deﬁnitions cofactor expansion (refer to 2.1)

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)

Determinant of a 2x2 matrix

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Deﬁnition: cofactor

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. Note that A. Is an !

(n-1)x(n-1) matrix

Since i and j can take any value from 1 to n there

are n Cofactors. We can therefore deﬁne a matrix

such that its (i,j) entry is

such matrix is called cofactor matrix (of A) we will

donote it Cof(A)

Deﬁnition:

Adjoint of A: Given A a nxn matrix, the adjoint of A is

the nxn matrix deﬁned as

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