This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: The cross product, matrices and determinants January 17, 2012 References: Marsden and Tromba Vector Calculus Definition 0.1. A 2 × 2 matrix is an array A = a 11 a 12 a 21 a 22 where the entry of the i th column and j th row a ij is a scalar. Definition 0.2. The determinant of a 2 × 2 matrix is  A  = a 11 a 22 a 12 a 21 . Example 0.1. A = 1 5 6 3 and det A = 3 30 = 27 . Definition 0.3. A 3 × 3 matrix is an array A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 where the entry of the i th column and j th row a ij is a scalar. Definition 0.4. The determinant of a 3 × 3 matrix A is given by det A = a 11 det a 2 2 a 23 a 32 a 33 a 12 det a 21 a 23 a 31 a 33 + a 23 det a 21 a 22 a 31 a 32 Definition 0.5. The cross product of two vectors a , b ∈ R 3 is denoted by a × b and is given by a × b = a 2 b 3 a 3 b 2 a 3 b 1 a 1 b 3 a 1 b 2 a 2 b 1 = det i j k a 1 a 2 a 3 b 1 b 2 b 3 = det a 2 a 3 b 2 b 3 i det a 1 a 3 b 1 b 3 j + det a...
View
Full Document
 Winter '08
 JackWaddell
 Determinant, Vector Calculus, Matrices, Scalar, Howard Staunton, a3 b2, a3 c3, a2 a3 b1

Click to edit the document details