Use Inverse Matrices to Solve Linear Systems 1

Use Inverse Matrices to Solve Linear Systems 1. 2. 3. Objectives To find the inverse of a square matrix To solve a matrix equation using inverses 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 Matrix • Identity Property of Matrix Multiplication

Exercise 1 •

Inverse Matrix

Exercise 2 •

Inverse Matrix (2 x 2)

Exercise 3 •

Exercise 4 •

Matrix Equations •

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 Objective 3

Exercise 7 Use an inverse matrix to solve the linear system.

Solving Systems using Inverses Step 1 Step 2 Step 3

Protip: Multiplying by Inverse When multiplying by an inverse matrix to solve a matrix equation, first multiply by the “subinverse” and then divide each element by the determinant. “Subinverse” 1 divided by the determinant

Exercise 8 Solve each system using inverse matrices.

Inverse Matrix (3 x 3) •

Inverse Matrix (3 x 3) •

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 1. 2. 3. Objectives To find the inverse of a square matrix To solve a matrix equation using inverses To solve a linear system using inverse matrices