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1313_section2o6

# 1313_section2o6 - Section 2.6 The Inverse of a Square...

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Section 2.6 – The Inverse of a Square Matrix 1 Section 2.6 - The Inverse of a Square Matrix In this section we discuss a procedure for finding the inverse of a matrix and show how the inverse can be used to help us solve a system of linear equations. Let A be a square matrix of size n. A square matrix 1 - A of size n such that n I A A AA = = - - 1 1 is called the inverse of A . Note: Not every square matrix has an inverse. A matrix with no inverse is called singular . Finding the Inverse of a Matrix Given the nxn matrix A : 1. Adjoin the nxn identity matrix I to obtain the augmented matrix ( I A | 2. Use a sequence of row operations to reduce ( I A | to the form ( B I | , if possible. The matrix B is the inverse of A . Matrices That Have No Inverses If there is a row to the left of the vertical line in the augmented matrix containing all zeros, then the matrix does not have an inverse. Example 1: Find the inverse of a. = 4 3 2 1 A .

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Section 2.6 – The Inverse of a Square Matrix 2 b. B =
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