1. Use Inverse Matrices to Solve Linear Systems
Notes 3.8 (Day 1)
Use Inverse Matrices to Solve Linear Systems

2. The inverse of the matrixis

3. Find the inverse of:

4. Find the inverse of:

5. Find the inverse of:

6. Find the inverse of:

7. Identity matrix
A matrix with 1’s on the main diagonal and 0’s elsewhere.
2 x 2 Identity Matrix
3 x 3 Identity Matrix
Just like the identity property of multiplication (anything times 1 is itself), in matrix algebra any matrix multiplied by the identity matrix is itself.

8. Solving matrix equations AX = B for the 2 x 2 matrix X.
Step 1: Find the inverse of A.
Step 2: Multiply both sides of the equation by the inverse of A.
Step 3: The identity matrix should appear on the left hand side of the equation, and on the right should be a 2 x 2 matrix.
Step 4: In matrix multiplication, anything multiplied by the identity matrix is itself.
Step 5: The solution is the remaining 2 x 2 matrix on the right hand side of the equation.

9. Solve the matrix equation AX = B for the 2 x 2 matrix X.

10. Solve the matrix equation AX = B for the 2 x 2 matrix X.

11. Solve the matrix equation AX = B for the 2 x 2 matrix X.

12. Homework:
P , 13-18