2.2 The Inverse of a Matrix. Example: REVIEW Invertible (Nonsingular)

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Presentation transcript:

2.2 The Inverse of a Matrix

Example: REVIEW

Invertible (Nonsingular)

Theorem 4 Example:

Theorem 5 Proof: Example: Use the inverse of the matrix to solve the system

Theorem 6 1. If is an invertible matrix, then is invertible: 2. If and are invertible matrices, then so is : 3. If is an invertible matrix, then so is :

Elementary Matrix obtained by performing a single elementary row operation on an identity matrix. Example:

Remark

Theorem 7

How to find : Example: Find the inverse of