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By Martin Julian Buerger

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A1 bl CI a2 62 C2 a3 b3 C3 out The minor of a1 is therefore out CHAPTER 1. VECTOR ANALYSIS 56 is associated with the minor of In the general nth-order determinant, the sign (-1)"j the element in the ith row and the jth column. The minor with its sign (-l)isj is called the cofactor. For the general determinant the value in terms of cofactors is given by n =Caij~ij forany IA~ i. 8) is called the Laplace development. Expanding it along the first row gives i = 1. For example, all a12 2 becomes +a12~12 lAl = a i j ~ '= j all~ll j=1 where ~ 1 =1 (-l)l+l la221 = aa2 and A12 = ( - I ) ' + ~ la21 1 = -a21.

Candela is the luminous intensity (in the perpendicular direction) of a surface of 1/600,000 square meter of a blackbody a t the temperature of freezing Platinum under a pressure of 101,325 N/m. 1 Appendix 11: Properties of Determinants Introduction This appendix is devoted to a summary of some essential properties of determinants. A determinant is a square array of quantities called elements which may be combined according to the rules given below. In symbolic form, we write The order of the above determinant is n.

1 = 1. (a) Show that the velocity of this particle is give11 by + where T = -i sin 0 + j cos 0. (b) Show that the acceleration of this particle is given by [@T T(&)2]. r + 0r7+2-- d ~ d O ]T a = -- dt" dtL dt dt C H A P T E R 1. VECTOR. ANALYSIS 52 (c) Identify the radial and tangential components of the velocity and acceleration, respectively. Identify the centripetal acceleration. The Coriolis17 acceleration is given by 2(dr/dt) ( d Q / d t ) ~ . 39 A force with x, y, and z components of 3,4, and 12 N, respectively, displaces an object from the point (1,2,3) to (2, -3,l).

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