Suggested languages for you:

Americas

Europe

Q8.1-17E

Expert-verifiedFound in: Page 437

Book edition
5th

Author(s)
David C. Lay, Steven R. Lay and Judi J. McDonald

Pages
483 pages

ISBN
978-03219822384

**Question:**** ****17. Choose a set \(S\) of three points such that aff \(S\) is the plane in \({\mathbb{R}^3}\) whose equation is \({x_3} = 5\). Justify your work.**

The set is \(S = \left\{ {\left( \begin{array}{l}0\\0\\5\end{array} \right),\left( \begin{array}{l}1\\0\\5\end{array} \right),\left( \begin{array}{l}1\\1\\5\end{array} \right)} \right\}\).

The set of three vectors that lie along the plane \({x_3} = 5\) must have 5 as their third entry and cannot be collinear.

The set of vectors that is not collinear cannot have a line as their affine hull.

One of the possible sets of three vectors discussed above is \(S = \left\{ {\left( \begin{array}{l}0\\0\\5\end{array} \right),\left( \begin{array}{l}1\\0\\5\end{array} \right),\left( \begin{array}{l}1\\1\\5\end{array} \right)} \right\}\).

94% of StudySmarter users get better grades.

Sign up for free