# lecture8 - Lecture 8 Matrices and Matrix Operations in...

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Unformatted text preview: Lecture 8 Matrices and Matrix Operations in Matlab Matrix operations Recall how to multiply a matrix A times a vector v : A v = parenleftbigg 1 2 3 4 parenrightbiggparenleftbigg- 1 2 parenrightbigg = parenleftbigg 1 · (- 1) + 2 · 2 3 · (- 1) + 4 · 2 parenrightbigg = parenleftbigg 3 5 parenrightbigg . This is a special case of matrix multiplication. To multiply two matrices, A and B you proceed as follows: AB = parenleftbigg 1 2 3 4 parenrightbiggparenleftbigg- 1- 2 2 1 parenrightbigg = parenleftbigg- 1 + 4- 2 + 2- 3 + 8- 6 + 4 parenrightbigg = parenleftbigg 3 5- 2 parenrightbigg . Here both A and B are 2 × 2 matrices. Matrices can be multiplied together in this way provided that the number of columns of A match the number of rows of B . We always list the size of a matrix by rows, then columns, so a 3 × 5 matrix would have 3 rows and 5 columns. So, if A is m × n and B is p × q , then we can multiply AB if and only if n = p . A column vector can be thought of as a p × 1 matrix and a row vector as a 1 × q matrix. Unless otherwise specified we will assume a vector v to be a column vector and so A v makes sense as long as the number of columns of A matches the number of entries in v . Printing matrices on the screen takes up a lot of space, so you may want to use > format compact Enter a matrix into Matlab with the following syntax: > A = [ 1 3 -2 5 ;-1-1 5 4 ; 0 1 -9 0] Also enter a vector u : > u = [ 1 2 3 4]’ To multiply a matrix times a vector A u use * : > A*u Since A is 3 by 4 and u is 4 by 1 this multiplication is valid and the result is a 3 by 1 vector. Now enter another matrix B using: > B = [3 2 1; 7 6 5; 4 3 2] You can multiply B times A : > B*A but A times B is not defined and > A*B will result in an error message....
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## This note was uploaded on 02/09/2012 for the course MATH 344 taught by Professor Young,t during the Fall '08 term at Ohio University- Athens.

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lecture8 - Lecture 8 Matrices and Matrix Operations in...

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