Inverse and Identity Matrices

Can only be used for square matrices. (2x2, 3x3, etc.)

Identity Matrix

identity – number used to keep a value the same

identity matrix – matrix used to keep a matrix the same

A*I = I*A = A

Inverse Matrix

inverse – number used to get the identity

inverse matrix – matrix used to get the identity matrix

A*A-1 = A-1*A = I

Inverse Matrix

Inverse Matrix

Inverse Matrix

Inverse Matrix

Solving Systems

3x – 5y = -26-x + 2y = 10

Solving Systems

3x – 5y = -26-x + 2y = 10

Solving Systems

3x – 5y = -26-x + 2y = 10

Solving Systems

3x – 5y = -26-x + 2y = 10

Solving Systems

3x – 5y = -26-x + 2y = 10

Solving Systems

3x – 5y = -26-x + 2y = 10

( -2 , 4 )

Practice

Solve the system using the inverse matrix.

x – y = 22x + 3y = 14