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Back to Orthogonal Projection Into a Line

Exercise 3

Avg difficulty 3.0

Although pictures guided our development of Definition 1.1, we are not restricted to spaces that we can draw. In R4\mathbb{R}^{4} project this vector into this line.

v⃗=(1213)ℓ={c⋅(−11−11)∣c∈R}\vec{v}=\begin{pmatrix}1\\ 2\\ 1\\ 3\end{pmatrix}\qquad\ell=\text{$\{\hskip 1.00006ptc\cdot\begin{pmatrix}-1\\ 1\\ -1\\ 1\end{pmatrix}\mid c\in\mathbb{R}\hskip 1.00006pt\}$}

Hefferon, Linear Algebra, Maps Between Spaces, Orthogonal Projection Into a Line, Exercise 3

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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.