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Subspaces

Applying the closure tests to subsets of R^2 and R^3 cut out by inequalities and products, producing counterexamples where addition or scaling escapes the set.

Matrix Theory and Linear Algebra, Subspaces

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3 exercises

Exercise 9.3.2

Consider the set of all vectors $\left[\begin{array}{c}x\\ y\end{array}\right]\in\mathbb{R}^{2}$ such that $x+y\geq 0$ . Is this a subspace of $\mathbb{R}^{2}$ ?

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Exercise 9.3.3

Consider the set of all vectors $\left[\begin{array}{c}x\\ y\end{array}\right]\in\mathbb{R}^{2}$ such that $xy=0$ . Is this a subspace of $\mathbb{R}^{2}$ ?

3.0

Exercise 9.3.8

Let $U=\left\{\left.\left[x,y,z\right]^{T}\in\mathbb{R}^{3}~{}\right|~{}\left|x\right|\leq 4\right\}$ . Is $U$ a subspace of $\mathbb{R}^{3}$ ?

3.0

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.