Explore the Power of Identity Matrix in Linear Algebra

1. Algebra 2 Before: You solved Linear Systems using Cramer’s Rule Now:___________________________________ __________________________________________Why? So you can find how many batches of a recipe to make

2. Identity matrix • Identity Matrix: The n x n identity matrix with 1’s on the _________________________________ and 0’s ________________ • If A is any A x A matrix and I is the n x n identity matrix, then AI = A and IA = A • Ex: 2 x 2 Identity Matrix 3 x 3 Identity Matrix

3. Inverse: Two n x n matrices A and B are inverses of each other if ________________________________ • That is AB = I and BA = I • The symbol for the inverse of A is A-1

5. Example 1

6. Example 2

8. Example 3

9. Guided Practice