{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

slide2-aug24

# slide2-aug24 - ECON 401 Matrices Siyang Xiong Rice...

This preview shows pages 1–8. Sign up to view the full content.

ECON 401: Matrices Siyang Xiong Rice University August 23, 2011 Xiong (Rice University) ECON 401 August 23, 2011 1 / 24

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

View Full Document
Matrice n equations of m variable a 11 x 1 C a 12 x 2 C ... C a 1 m x m D b 1 (1) a 21 x 1 C a 22 x 2 C ... C a 2 m x m D b 2 ... a n 1 x 1 C a n 2 x 2 C ... C a nm x m D b n (1) can be represented as follows: 2 4 a 11 ... a 1 m ... ... ... a n 1 ... a nm 3 5 2 4 x 1 ... x m 3 5 D 2 4 b 1 ... b n 3 5 Xiong (Rice University) ECON 401 August 23, 2011 2 / 24
matrice consider a n ° m matrice A , A D 2 4 a 11 ... a 1 m ... ... ... a n 1 ... a nm 3 5 , for example b A D ° 1 2 4 2 0 2 ± row vectors, denoted as A r i , are de°ned as: b A r i D ² a i 1 ... a im ³ ; b A r 1 D ² 1 2 4 ³ ; b A r 2 D ² 2 0 2 ³ . sometimes we write, A D 2 4 A r 1 ... A r n 3 5 . Xiong (Rice University) ECON 401 August 23, 2011 3 / 24

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

View Full Document
matrice consider a n ° m matrice A , A D 2 4 a 11 ... a 1 m ... ... ... a n 1 ... a nm 3 5 , for example b A D ° 1 2 4 2 0 2 ± column vectors, denoted as A c j , are de°ned as: A c j D 2 4 a 1 j ... a nj 3 5 ; b A c 1 D ° 1 2 ± ; b A c 2 D ° 2 0 ± ; b A c 3 D ° 4 2 ± . sometimes we write, A D ² A c 1 ... A c m ³ Xiong (Rice University) ECON 401 August 23, 2011 4 / 24
addition of matrices given two n ° m matrices A and B , A C B D 2 4 a 11 C b 11 ... a 1 m C b 1 m ... ... ... a n 1 C b n 1 ... a nm C b nm 3 5 for example: A D ° 1 2 4 2 0 2 ± and B D ° 3 2 1 0 4 2 ± , A C B D ° 1 C 3 2 C 2 4 C 1 2 C 0 0 C 4 2 C 2 ± D ° 4 4 5 2 4 4 ± Xiong (Rice University) ECON 401 August 23, 2011 5 / 24

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

View Full Document
multiplication of matrices given a n ° m matrice A and a m ° k matrice B , AB D 2 6 6 6 6 4 A r 1 ± B c 1 ... A r 1 ± B c k ... ... ... ... A r i ± B c j ... ... ... ... A r n ± B c 1 ... A r n ± B c k 3 7 7 7 7 5 is a n ° k matrice, D 2 6 6 6 6 4 P m h D 1 A 1 h ± B h 1 ... P m h D 1 A 1 h ± B hk ... ... ... ... P m h D 1 A ih ± B hj ... ... ... ... P m h D 1 A nh ± B h 1 ... P m h D 1 A nh ± B hk 3 7 7 7 7 5 . Xiong (Rice University) ECON 401 August 23, 2011 6 / 24
multiplication of matrices for example: A D 2 4 1 ² 1 2 0 1 3 3 5 and B D ° 1 2 4 2 0 2 ± : AB D 2 4 1 ² 1 2 0 1 3 3 5 ° 1 2 4 2 0 2 ± D 2 4 1 ° 1 C .

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 ]}