Linear Algebra - Row-Addition Matrix

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1 - About

<math> \begin{bmatrix} 1 & 0 & 0 \\ \hline 2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix} </math> is called an elementary row-addition matrix as:

<MATH> \begin{bmatrix} 1 & 0 & 0 \\ \hline 2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix} \underbrace{ \begin{bmatrix} b_1 \\ \hline b_2 \\ \hline b_3 \end{bmatrix}}_{Matrix B} = \begin{bmatrix} b_1 \\ \hline 2 b_1 + b_2 \\ \hline b_3 \end{bmatrix} </MATH>

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3 - Property

3.1 - Invertible

A row-addition matrix is invertible.

<math> \begin{bmatrix} 1 & 0 & 0 \\ \hline 2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix} </math> and <math> \begin{bmatrix} 1 & 0 & 0 \\ \hline -2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix} </math> are inverse.

linear_algebra/row_addition.txt · Last modified: 2013/08/21 17:54 by gerardnico