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Q8.1-17E

Expert-verified
Found in: Page 437

### Linear Algebra and its Applications

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

See the step by step solution

## Step 1: Describe the given statement

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.

## Step 2:  Draw a conclusion

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