Differential Equations and Linear Algebra (4th Edition)

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

Chapter 4 - Vector Spaces - 4.4 Spanning Sets - Problems - Page 283: 27

Answer

See below

Work Step by Step

Given: $A=\begin{bmatrix} 2 & -4\\1 & 2\\-3 & 5 \end{bmatrix}$ Obtain: $\begin{bmatrix} 2 & -4\\1 & 2\\-3 & 5 \end{bmatrix}\begin{bmatrix} x_1\\x_2 \end{bmatrix}=0$ We have the system: $2x_1-4x_2=0\\ x_1+2x_2=0\\ -3x_1+5x_2=0\\ \rightarrow x_1=x_2=0$ Then $N(A)=(x_1,x_2) \in R^2:x_1=x_2=0)$ Hence, $N(A)=span (0,0)$
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