4.4 Identity & Inverse Matrices

IdentityWhat number is the multiplication identity for

real numbers?For matrices, n x n--square matrices, has 1’s

on main diagonal and zeros elsewhere2 x 2 3 x 3

1 0

0 1

1 0 0

0 1 0

0 0 1

InverseWhen multiply 2 matrices, A & B, in both

orders, you get the identity matrixAB = IBA = I2 x 2

A a b

c d

1 1A , det 0

A

d b

c a

EXAMPLESFind the inverse of the given matrices1) 2)

3 2

2 4

6 1

8 2

Solving Matrix EquationsFind the inverse of the matrix that is being

multiplied by XMultiply both sides of the equation by that

inverseMake sure to always write the inverse matrix

1st (on left side)

1 1

1

AX B

A AX A B

X A B

EXAMPLESSolve the matrix equation1) 2)3 4 3 8

5 7 2 2X

1 2 7 2

4 7 1 9X

Inverses of 3 x 3Use a graphing calculatorEnter MatrixChoose matrixUse key and press enter

HW: p227-228 #14-36 even, 37-39

1x

0 1 1

2 0 1

1 3 3

A

1 2 3

3 1 2

3 1 1

B