1. Solving Linear Systems Using Inverse Matrices
Notes 11.3 (Day 1)
Solving Linear Systems Using Inverse Matrices

2. 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.

3. How to prove that matrices are inverses:
Step 1: Multiply the A ∙ A-1
Step 2: The result should be an identity matrix.
Step 3: Multiply A-1 ∙ A
Step 4: The result should be an identity matrix.

4. Show that the given matrices are inverses.

5. Show that the given matrices are inverses.

6. Homework:
P , 12-25