Exercise 2.6.14

Avg difficulty 3.0

Decompose the vector $\mathbf{v}$ into $\mathbf{v}=\mathbf{a}+\mathbf{b}$ where $\mathbf{a}$ is parallel to $\mathbf{u}$ and $\mathbf{b}$ is orthogonal to $\mathbf{u}$ .

\mathbf{v}=\left[\begin{array}{r}3\\ 2\\ -5\end{array}\right],\quad\mathbf{u}=\left[\begin{array}{r}1\\ -1\\ 2\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Vectors in Rn, The dot product, Exercise 2.6.14

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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.