MATH 133 Lecture Notes - Laplace Expansion
DepartmentMathematics & Statistics (Sci)
Course CodeMATH 133
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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
Determinant of a 2x2 matrix
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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 !
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)
Adjoint of A: Given A a nxn matrix, the adjoint of A is
the nxn matrix deﬁned as
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