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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online