Chapter 4 Section 4: Inverse and Identity Matrices 1

Remember: The additive identity is 0, a + (-a) = 0 so a and –a are additive inverses The multiplicative identity is 1, Similarly there are identity matrices and inverse matrices 2

The inverse of A is written A -1 and makes AA -1 =I I, the identity matrix, is a square matrix with ones on the diagonal and zeros everywhere else. This is a determinate This is a matrix Note: a and d switch, but b and c change signs. Find the inverse of a 2 X 2 matrix This is an inverse matrix 3

2*5-3*4=-2 Remember to find the determinant and rearrange A: 

Multiply A and A -1 from the previous slide. A A -1 = 5

1. Find the determinant 2. Rearrange A 6

With the calculator, we can easily find the inverse of a 3x3 matrix. 7

HW: p 227#15-36x3 8

Using the Inverse to Solve a Matrix Equation This is A*X=B To solve for X, multiply both sides of the equation by A -1 3*7-9*2=3 9

Multiply both sides by the inverse 10