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Exercise 3.2.2

Avg difficulty 3.0

Consider the following vector equation for a plane in R4\mathbb{R}^{4}:

[xyzw]=[1200]+t [1001]+s [−1−110].\left[\begin{array}{c}x\\ y\\ z\\ w\end{array}\right]=\left[\begin{array}{r}1\\ 2\\ 0\\ 0\end{array}\right]+t\,\left[\begin{array}{r}1\\ 0\\ 0\\ 1\end{array}\right]+s\,\left[\begin{array}{r}-1\\ -1\\ 1\\ 0\end{array}\right].

Find a new vector equation for the same plane by doing the change of parameters t=1−r1t=1-r_{1}, s=r1+r2s=r_{1}+r_{2}.

Selinger, Matrix Theory and Linear Algebra, Lines and planes in Rn, Planes, Exercise 3.2.2

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.