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Explore the Power of Identity Matrix in Linear Algebra

Dive into the concept of Identity Matrix in Algebra 2. Learn how to use it to determine the number of recipe batches needed. Understand the properties of Identity Matrix and its role in solving equations. Master the fundamentals of Inverse Matrices through examples and guided practice.

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Explore the Power of Identity Matrix in Linear Algebra

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  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

  4. Example 1

  5. Example 2

  6. Example 3

  7. Guided Practice

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