This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 18.02 (Spring 2009): Lecture 3 Matrices. Inverse Matrices February 6 Reading Material: From Course Notes M. Last time: Cross product and determinant Today: Matrices and Inverse Matrices Recall: A matrix A is defined as A = a 11 a 12 ··· a 1 n . . . a m 1 a m 2 a mn = ( a i,j ) n = # columns and m = # rows hence A is a m × n matrix. 2 Matrix Arithmetic • Addition: If A, B are m × n matrices then A + B is obtained by adding entries in the same location . • Multiplication by scalar: Given a matrix A = ( a ij ) and a scalar c we define the new matrix cA as cA = ( ca ij ) , This means that we have to multiply every entry of A by the scalar c . 1 • Mutiplication of two matrices: If A is a m × n and B is a n × s matrix then A · B is a m × s matrix such that its c ij entry is given by ( a i 1 a i 2 ··· a in ) · b 1 j b 2 j . . . b nj = c ij i = 1 , . . . , m j = 1 , . . . , s c ij = row i · col j = n X k =1 a ik b kj ↓ dot product so A ( m × n ) times...
View
Full Document
 Spring '08
 Auroux
 Linear Algebra, Multiplication, #, Invertible matrix

Click to edit the document details