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2.5 The Gauss-Jordan Method for Calculating Inverses

2.5 The Gauss-Jordan Method for Calculating Inverses. Gauss-Jordan Method for Inverses. Gauss-Jordan Method for Inverses. Step 1: Write down the matrix A , and on its right write an identity matrix of the same size.

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2.5 The Gauss-Jordan Method for Calculating Inverses

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  1. 2.5 The Gauss-Jordan Method for Calculating Inverses • Gauss-Jordan Method for Inverses

  2. Gauss-Jordan Method for Inverses • Step 1: Write down the matrix A, and on its right write an identity matrix of the same size. • Step 2: Perform elementary row operations on the left-hand matrix so as to transform it into an identity matrix. These same operations are performed on the right-hand matrix. • Step 3: When the matrix on the left becomes an identity matrix, the matrix on the right is the desired inverse.

  3. Example Inverses • Find the inverse of Step 1: Step 2:

  4. Example Inverses (2) Step 3:

  5. Summary Section 2.5 • To calculate the inverse of a matrix by the Gauss-Jordan method, append an identity matrix to the right of the original matrix and perform pivots to reduce the original matrix to an identity matrix. The matrix on the right will then be the inverse of the original matrix. (If the original matrix cannot be reduced to an identity matrix, then the original matrix does not have an inverse.)

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