mthsc206-fall-2010-notes-13.4

mthsc206-fall-2010-notes-13.4 - 13.4 The Cross Product...

This preview shows pages 1–2. Sign up to view the full content.

13.4 The Cross Product Algebraic Description Defnition 13.4.1 An m × n matrix is a rectangular array with m rows and n columns of objects. A generic m × n matrix A has the form A = a 11 a 12 a 13 ··· a 1 n a 21 a 22 a 23 a 2 n a 31 a 32 a 33 a 3 n . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 a mn . Defnition 13.4.2 The determinant of a 2 × 2 matrix A = ± a 11 a 12 a 21 a 22 ² , denoted either det( A ) or | A | , is | A | = a 11 a 22 - a 12 a 21 . The determinant of a 3 × 3 matrix A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 is given by | A | = a 11 ³ ³ ³ ³ a 22 a 23 a 32 a 33 ³ ³ ³ ³ - a 12 ³ ³ ³ ³ a 21 a 23 a 31 a 33 ³ ³ ³ ³ + a 13 ³ ³ ³ ³ a 21 a 22 a 31 a 32 ³ ³ ³ ³ = a 11 ( a 22 a 33 - a 23 a 32 ) - a 12 ( a 21 a 33 - a 23 a 31 )+ a 13 ( a 21 a 32 - a 22 a 31 ) . Example 13.4.1 Find the determinant of the matrix (a) ± 14 - 27 ² and (b) 1 0 4 0 2 6 2 1 0 . Defnition 13.4.3 Let u = <u 1 ,u 2 3 > and v = <v 1 ,v 2 3 > be two vectors in V 3 . The cross product of u with v , denoted u × v , is given by u × v = ³ ³ ³ ³ ³ ³ i j k u 1 u 2 u 3 v 1 v 2 v

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

mthsc206-fall-2010-notes-13.4 - 13.4 The Cross Product...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online