Chapter 2.3 Determinants-Properties

For each i 1 2 n dene a map ti rn r by v1

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Unformatted text preview: e a map Ti : Rn → R by v1 . . . vi −1 Ti (x) = det x vi . . . vn−1 Ti (x ) returns the value of the determinant of the n × n matrix A with rows v1 , · · · , vi −1 , x, vi , . . . , vn−1 (x is the i th row of A). Outline Linearity of the Determinant Determinants and Invertibility Determinants and Products Determinants and Inverses The Linearity of the Determinant Map Theorem For each i ∈ {1, 2, . . . , n}, the map Ti : Rn → R defined above is linear: Ti (x + y) = Ti (x) + Ti (y) and Ti (λx) = λTi (x). We say that the determinant is linear in the i th row and linear in the i th column. Outline Linearity of...
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