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Section 13-5 : Inverses of Matrices Objectives: 1)Background – what are inverses and why find them. 2)Process for finding the inverse of a 2x2 matrix.

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Background: Inverses of matrices are useful for solving systems of equations. To introduce the concept, consider the following system of equations; this system can be written as a matrix. The solution to this system can also be written as a matrix. The process for using an inverse to solve a system of equation is similar to the process for solving the following simple equation.

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The result of multiplying 5 by its reciprocal was 1. The result of multiplying a matrix by its inverse (similar to a reciprocal) is the identity matrix. The question becomes, how do we find the inverse matrix?? Note: If a matrix is defined as A, then its inverse is defined as A -1. Background (Continued)

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Your book (see pg. 590) provides a formula for finding the inverse of a 2x2 matrix. The formula is: Example: Finding the Inverse Matrix of a 2x2

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Is the product of a matrix and its inverse the identity matrix? Silly Question: What is the identity matrix for a 3x3 matrix? Check

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Multiplicative inverse and solving matrix equations

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