Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.5 Exercises - Page 48: 21

Answer

let $t$ represent a parameter. The line will go through $p$ parallel to $t*(q-p)$. $\mathbf{x}=\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}=\begin{bmatrix}2\\-5\end{bmatrix}+t\begin{bmatrix}-5\\6\end{bmatrix}$

Work Step by Step

$\mathbf{p}=\begin{bmatrix}2\\-5\end{bmatrix}$ $\mathbf{q}=\begin{bmatrix}-3\\1\end{bmatrix}$ let $t$ represent a parameter. The line $M$ will go through $p$ parallel to $t*(q-p)$. $\mathbf{x}=\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}=\begin{bmatrix}2\\-5\end{bmatrix}+t\begin{bmatrix}-3-2\\1-(-5)\end{bmatrix}=\begin{bmatrix}2\\-5\end{bmatrix}+t\begin{bmatrix}-5\\6\end{bmatrix}$
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