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Understanding Determinants in Linear Algebra: Properties and Applications

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  1. Lecture 18 • Determinants det(A) square matrix • Properties Linear Algebra---Meiling CHEN

  2. Properties : • Exchange rows reverse sign of det • 2 equal rows  det=0 (exchange rows get same matrix only probability is 0) Linear for each row Linear Algebra---Meiling CHEN

  3. Subtract l*row i from row j det does not change • 6 row of zeros  det(A)=0 • 7. Product of Pivots One of advantage of LU factorization By elimination we can kill these Linear Algebra---Meiling CHEN

  4. Zero row • 8. when A is singular • when A is invertible • 9 • 10. A=LU Linear Algebra---Meiling CHEN

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