We introduce the cofactor expansion definition of the determinant of a square matrix of any size, also called the Laplace Expansion. This recursive definition involves two new terms: minors and cofactors. The minor, Mij, of the entry aij is the determinant of the submatrix remaining when the ith row and jth column are deleted. Then, the cofactor of the entry aij is (1)^(i+j)*Mij. We'll do an example of finding all cofactors of a 2x2 matrix and using the cofactor expansion to find the determinant of the 2x2 matrix, then we will use the cofactor expansion to find the determinant of a 3x3 matrix along a row and then along a column. #linearalgebra

Minors and Cofactors:    • Minors and Cofactors of a Matrix | Li...  

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

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0:00 Intro
0:50 Minors and Cofactors
1:43 Cofactors of a 2x2 Matrix
3:45 Cofactor Expansion Definition of Determinants
5:18 2x2 Determinant by Cofactor Expansion
7:01 3x3 Determinant by Cofactors along a Row
10:52 3x3 Determinant by Cofactors along a Column
13:26 Conclusion

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