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Addition

Adding vectors component by component, and deriving rearrangement identities from the axioms of vector addition with every step justified.

Matrix Theory and Linear Algebra, Addition

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2 exercises

Exercise 2.2.1

Find $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]+\left[\begin{array}{c}1\\ 5\\ 1\end{array}\right]+\left[\begin{array}{c}-1\\ 2\\ -4\end{array}\right]$ .

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Exercise 2.2.2

Use the properties of vector addition from Proposition 2.12 to show the following equalities. Justify every step.

$(\mathbf{u}+\mathbf{v})+\mathbf{w}=(\mathbf{v}+\mathbf{w})+\mathbf{u}$ .
$(\mathbf{u}+\mathbf{0})+(\mathbf{v}+(-\mathbf{u}))=\mathbf{v}$ .

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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.