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Exercise 24

Avg difficulty 3.0

Which trivial subspace is the span of the empty set? Is it

{(000)}⊆R3,or{0+0x}⊆P1,\text{$\{\hskip 1.00006pt\begin{pmatrix}0\\ 0\\ 0\end{pmatrix}\hskip 1.00006pt\}$}\subseteq\mathbb{R}^{3},\quad\text{or}\quad\text{$\{\hskip 1.00006pt0+0x\hskip 1.00006pt\}$}\subseteq\mathcal{P}_{1},

or some other subspace?

Hefferon, Linear Algebra, Vector Spaces, Subspaces and Spanning Sets, Exercise 24

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.