Differential Equations and Linear Algebra (4th Edition)

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

Chapter 3 - Determinants - 3.2 Properties of Determinants - Problems - Page 219: 23

Answer

The given system has a unique solution if and only if $k \ne \pm 2$

Work Step by Step

$A=\begin{bmatrix} 1 &k\\ k &4 \end{bmatrix}$ $x=\begin{bmatrix} x_1\\ x_2 \end{bmatrix}$ $C=\begin{bmatrix} b_1\\ b_2 \end{bmatrix}$ $\rightarrow \det A=4-k^2$ The given system has a unique solution if and only if $\det A\ne0$ $4-k^2 \ne 0$ Hence, $k \ne \pm 2$
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