MA 265 LECTURES 9-11

week 4 sitinematrieerations I m row's damn I J aim ex 223 6 diagonal matrix square matrix zeros except on main diagonal I zero matrix ex 100000 00000 00000 identity matrix square matrix n'son main diagonal ex 5 1898 001 rules matrices are equal if they have same size and corresponding elements additionand subtraction on same size matrices multiplication row column rule agility I AB BA

matrix power must be a square otherwise not defined ex Af At E AAA E E Es t.FM sIne transpose ofA swap rows and columns ex af Eli properties AT T A At B T AT BT FEE at

intimate'mersmetamatrix scaler inverse 5 1.5 1 and 5.5 1 1 5 is the inverse of thescaler 5 matrix inverse A A I and AA i T A 1 is the inverseofmatrix A A must be square Not everysquare matrixhas an inverse if A has an inverse a is invertible otherwise a is singular 2 2 example I EEE thentisiEIntétiite determinant ex A I deta O so A exist A 1 12 34 112 3212 AA I 3 12 32 1 I I A A 112 3212 131 1 I X 8 7 6 2 2 5 7 4 2 1 8 4 Y 3 IF I A 3230 5 8 13 A 5 13 Ef