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Chapter 1.4 InverseMatrix

# Chapter 1.4 InverseMatrix - Outline Identity Matrices The...

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

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Outline Identity Matrices Inverse of a Matrix Outline 1 Identity Matrices 2 Inverse of a Matrix The Inverse of a Matrix Inverses, Products, and Powers
Outline Identity Matrices Inverse of a Matrix Identity Matrix Definition For any natural number n , let I n denote the n × n matrix whose a ij entry is 1 if i = j and 0 if i 6 = j . That is, I n = 1 0 · · · 0 0 1 · · · 0 . . . . . . . . . 0 0 · · · 1 I n is called the n × n identity matrix .

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Outline Identity Matrices Inverse of a Matrix The Identity Matrix Theorem For any m × n matrix A, AI n = A = I m A. That is, I n is a left multiplicative identity, and I m is a right multiplicative identity on the set of m × n matrices. Example Demonstrate the theorem for 2 × 4 matrices: A = a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 Theorem If A is an n × n matrix and R is the row-reduced echelon form of A, then either R contains a row of zeros or R = I n .
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