Overview Definitions Basic matrix operations (+, -, x) Determinants and inverses

Some Definitions … Zero Matrix Identity Matrix Diagonal Matrix I A = A I = A

Basic Operations Addition, Subtraction, Multiplication Just add elements Just subtract elements Multiply each row by each column

Multiplication Is AB = BA? Maybe, but maybe not! Is multiplication commutative? Try for the 2 matrices below

Multiplication Is AB = BA? Multiplication is NOT commutative AB = BA

Inverse of a Matrix Identity matrix: AI = A Some matrices have an inverse, such that: AA -1 = I

Inverse of a 2x2 Matrix

Matrix Inverse (Intro) A A -1 = A -1 A = I Properties A -1 only exists if A is square (n x n)

Determinant of a 2x2 Matrix The determinant of the matrix A is denoted |A|. Matrix A has no inverse whenever |A|= 0. A matrix with no inverse is SINGULAR. E.g., so an inverse exists, so no inverse exists

Inverse of a 2x2 Matrix AA -1 = I If = 0, then A has no inverse –A is SINGULAR E.g.

Inverse of a 2x2 Matrix AA -1 = I If |A| = 0, then A has no inverse –A is SINGULAR The 2x2 identity matrix