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Q14E

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

**Questions: Let \({F_{\bf{1}}}\) and \({F_{\bf{2}}}\) be 4-dimensional flats in \({\mathbb{R}^{\bf{6}}}\), and suppose that \({F_{\bf{1}}} \cap {F_{\bf{2}}} \ne \phi \). What are the possible dimension of \({F_{\bf{1}}} \cap {F_{\bf{2}}}\)?**

The dimension *D* of the solution set is, \(2 \le D \le 4\).

\({F_1}\) and \({F_2}\) have complete overlap, then \({F_1}\), \({F_2}\) have four **dimensions**.

As there is **six-dimensional space**, at the minimum, they have \(\left( {6 - 4 = 2} \right)\) dimensions. So, the range of dimensions is shown below:

\(2 \le D \le 4\)

Thus, the dimension of the solution set is from 2 to 4.

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