53 Determinants and Cramer’s Rule

determinant is 13 ©l R2w0i1 T2q yK lu RtBaJ wSGo if st 9wia 6rBe J mLJL lC B f 3 fA 2l2lF CreiEgHhQtRsJ 2r oe rs re Gr Fv je hdg N m 2M AaHdreM Bw2iJt1hb LIon afPi Onoi et QeK GAjl8gIe jb Hrfa Q t2 6

Determinants of 2×2 Matrices Date Period

16) Give an example of a 2×2 matrix whose determinant is 13 ©v l2K0w1X9h qKzuxtZav aSxocf_twwjairXes [LuLyC^ I v YAMlUln rrVi\g`hvtXse erKessjeDrgvGeFdm Z Z xMJaDdzek Dwbiit^hy HIGnCfjiZnRiItce_ eAplUgyeQbXrTar R2r

Determinanter for -matricer

Determinanter for n n-matricer Determinant for 2 2-matricer det a b c d := ad bc: Lad A = [a ij] vˆre en n n matrix Undermatricen A ij er den (n 1) (n 1) matrix

DETERMINANTS

2 2 a b a b ≠ or, a 1 b 2 – a 2 b 1 ≠ 0, then the system of linear equations has a unique solution) The number a 1 b 2 – a 2 b 1 which determines uniqueness of solution is associated with the matrix 1 1 2 2 A a b a b = and is called the determinant of A or det A Determinants have wide applications in Engineering, Science, Economics

53 Determinants and Cramer’s Rule

The formulas expand a 3 3 determinant in terms of 2 2 determinants, along a row of A The attached signs 1 are called the checkerboard signs, to be de ned shortly The 2 2 determinants are called minors of the 3 3 determinant jAj The checkerboard sign together with a minor is called a cofactor

DETERMINANTS EXERCICES - bagbouton

2 2 2 n n n n a a a a a a A a a a = ∈ ⋯ ⋯ ⋯ ⋯ ⋮ ⋮ ⋮ ℝ ⋮ ⋮ ⋮ ⋯ ⋯ M non nulle 1 Préciser le rang de la matrice A 2 Donner une condition nécessaire et suffisante pour que A soit la matrice d’un projecteur 3 On pose B A tr A I= −2 n Calculer le déterminant de B 4 Donner une condition nécessaire et suffisante

Some proofs about determinants - UCSD Mathematics

These notes are written to supplement sections 2 1 and 2 2 of the textbook Linear Algebra with Applications by S Leon for my Math 20F class at UCSD In those sections, the deﬂnition of determinant is given in terms of the cofactor expansion along the ﬂrst row, and then a theorem (Theorem 2 1 1) is stated

Chapitre 3 : Déterminants

1 2 Propriétés du déterminant Lycée du Hainaut Remarque 1 (i) Lorsque n ∈{2,3}, on retrouve la notion vue en TSI 1 (ii) Si n =2 et K =R, le déterminant de la matrice dont on note (u,v)les colonnes est l’aire algébrique du

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