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Chapter 1.4 ElementaryMatrices

Chapter 1.4 ElementaryMatrices - Outline Elementary Matrix...

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Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Elementary Matrices Math 2270 K. J. Platt, Ph.D. Department of Mathematics Snow College Spring 2014

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Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Outline 1 Elementary Matrix 2 Inverse of an Elementary Matrix 3 The Inverse of a Matrix Properties of an Invertible Matrix Finding the Inverse of a Matrix
Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Elementary Matrix Definition An n × n matrix E is called an elementary matrix if E is obtained from I n via exactly one elementary row operation. Example Discuss the following elementary matrices: E 1 = - 2 0 0 1 , E 2 = 0 0 1 0 1 0 1 0 0 , E 3 = 1 0 0 0 0 1 0 0 0 0 1 0 0 7 0 1 I n

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Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Elementary Matrices and Elementary Row Operations Theorem If A is an m × n matrix and E is an elementary n × n matrix, then EA is the m × n matrix obtained by performing the same
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