Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.4 Row-Echelon Matrices and Elementary Row Operations - Problems - Page 156: 23

Answer

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Work Step by Step

$\begin{bmatrix} 3 & 5 &-2\\ 2 & 3 & -7\\ -2 & -1 & 1 \end{bmatrix} \approx^1\begin{bmatrix} 1 & 2 &-5\\ 0 & -1 & 3\\ 0 & 3& -9 \end{bmatrix} \approx^2 \begin{bmatrix} 1 & 2 &-5\\ 0 & 1 & -3\\ 0 & 3& -9 \end{bmatrix} \approx^3 \begin{bmatrix} 1 & 0 &1\\ 0 & 1 & -3\\ 0 & 0&0 \end{bmatrix}$ Rank (A)= 2 The last matrix is in a row-echelon form. $A_{21}(-1),A_{12}(-2),A_{13}(2)$ $M_2(-1)$ $A_{21}(-2),A_{23}(-3)$
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