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Section 8.5 Theory
Subsection 8.5.1 Basic properties of determinants
The following justifies our definition of the determinant as the common value of all cofactor expansions of a matrix.
Theorem 8.5.1 . Uniformity of cofactor expansions.
Every cofactor expansion of a given square matrix, whether along a row or a column, evaluates to the same value.
Proof. The proof of this theorem is beyond the scope of this course; instead see [
2 ,
3 ].
Finally, let’s record the determinants of special forms of matrices we discussed in
Subsection 8.3.5 . However, we omit the proofs since we have already considered in detail the patterns behind the proofs in that earlier discussion.
Proposition 8.5.2 . Determinants of special forms.
