1. Unit 1.11 – Use Inverse Matrices to Solve Linear Systems

2. Unit 1 – Algebra: Linear Systems, Matrices, & Vertex-Edge Graphs
1.11 – Use Inverse Matrices to Solve Linear Systems
Georgia Performance Standard:
MM3A4b
Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.
MM3A5a
Represent a system of linear equations as a matrix equation.
MM3A5b
Solve matrix equations using inverse matrices

3. Vocabulary
The n x n identity matrix is a matrix with 1’s on the main diagonal and 0’s elsewhere. If A is any n x n matrix and I is the n x n identity matrix, then AI = A and IA = A.
2 x 2 Identity Matrix
3 x 3 Identity Matrix

4. Vocabulary
Two n x n matrices A and B are inverses of each other if their product (in both orders) is the n x n identity matrix. That is, AB = I and BA = I. An n x n matrix A has an inverse if and only if det A ≠ 0. The symbol for the inverse of A is A-1

5. Inverse of 2 x 2 Matrix Steps:
Same as finding the determinant just put it under 1.
Flip and Negatify! (Math word…sort of)

6. Example for finding the inverse of a 2 x 2 matrix…

7. Try this…
Page 54: 1-3
Guided Practice

8. Solve a Matrix Equation
Steps:
Find the inverse of the matrix that is next to the variable.
Multiply both sides of the equation by the inverse
Left side will cancel

9. Example