Скачать с ютуб The Cofactor Definition of Determinants (Laplace Expansion Explained) | Linear Algebra в хорошем качестве

The Cofactor Definition of Determinants (Laplace Expansion Explained) | Linear Algebra

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   Join Wrath of Math to get exclusive videos, music, and more:    / @wrathofmath   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 ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon! Outro music is mine. You cannot find it anywhere, for now. Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020