Lecture16bw

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

This preview shows pages 1–4. Sign up to view the full content.

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

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

View Full Document
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
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.

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.

## This note was uploaded on 11/01/2009 for the course ENGLISH 7 taught by Professor Sengupta during the Spring '09 term at Berkeley.

### Page1 / 6

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online