lecture3-09[1]

lecture3-09[1] - Math 18.02 (Spring 2009): Lecture 3...

Info iconThis preview shows pages 1–3. 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: 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

Page1 / 6

lecture3-09[1] - Math 18.02 (Spring 2009): Lecture 3...

This preview shows document pages 1 - 3. Sign up to view the full document.

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