Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve a linear system using inverse matrices Warm-Up Imagine you lived in a world that never defined subtraction or division. What would you do to get the same results? Objective 1 You will be able to find the inverse of a square matrix Identity Matrix Identity Property of Matrix Multiplication Exercise 1 Inverse Matrix Exercise 2 Inverse Matrix (2x2) Exercise 3 Exercise 4 Matrix Equations How to solve a matrix equation Since matrix multiplication is not commutative, you must remember to always multiply on the same side. Exercise 5 Exercise 6 You will be able to solve a linear system using inverse matrices Exercise 7 Use an inverse matrix to solve the linear system. Step 3Step 2 Step 1 Solving Systems using Inverses Protip: Multiplying by Inverse When multiplying by an inverse matrix to solve a matrix equation, first multiply by the sub- inverse and then divide each element by the determinant. Sub- inverse 1 divided by the determinant Exercise 8 Solve each system using inverse matrices. Inverse Matrix (3x3) Exercise 9 Exercise 10 Exercise 11 Solve the system using inverse matrices. Exercise 12 Solve the system using inverse matrices. 3.8: Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve a linear system using inverse matrices