Lecture16bw - LECTURE 16 TWO-DIMENSIONAL ARRAYS > x = 11 21...

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LECTURE 16 atrices Matrices atrix multiplication Matrix multiplication Solution of linear equations 1 E7, Fall 2008, M. Frenklach TWO-DIMENSIONAL ARRAYS >> x = [ 11 12 13 1 22 23 21 23 ]; >> x' 1 21 11 12 22 transposed atrix 13 23 matrix 2 DOT PRODUCT 1 m1 1 1 = * a 1 a 2 a 3 ••• b m + + + m m b a b a b a 2 2 1 1 " 1 b 2 b 3 = = m i i i b a 1 ••• 3 Multiplication of matrix and array m 1 c 1 b 1 4 4 = * 2 2,1 m b 2 b 3 ••• ( ) 2,1 2,1 1,1 2,2 2,3 3,1 ca b a b a b =+ + + 4
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MATRIX MULTIPLICATION m 3 3 = * c 4 m 4 2 2 , 1 1 ( ) 2,1 2,1 1,1 2,2 2,3 3,1 ca b a b a b =+ + + 5 MATRIX MULTIPLICATION 1 m 1 m = * m m 6 SIMULTANEOUS LINEAR EQUATIONS y y ax b c x d + x yc 7 DETERMINANTS + 2 3 * 2 4 * 1 4 3 2 1 ) ( ; 4 3 2 1 = = = = A A d + 13 12 11 a a a 12 11 a a 33 32 31 23 22 21 a a a a a a 32 31 22 21 a a a a in MATLAB: >> det(A) 8
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SIMULTANEOUS LINEAR EQUATIONS ax b yp += y dy q = cx x ab 0 d = if there is no solution cd 9 EXAMPLE: ELECTRIC CIRCUIT = 10 = 5 R 10 Ω R 5 Ω 1 2 3 V 1 = 200 V R = 10 Ω R = 5 Ω 4 5 6 R = 15 Ω R = 20 Ω V 6 = 0 V Background . Two laws are involved: irchhoff’s law he sum of all currents flowing into a node is zero Kirchhoff s law : The sum of all currents flowing into a node is zero.
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This note was uploaded on 11/01/2009 for the course ENGLISH 7 taught by Professor Sengupta during the Spring '09 term at Berkeley.

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Lecture16bw - LECTURE 16 TWO-DIMENSIONAL ARRAYS > x = 11 21...

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