Skip to main content
\(\require{cancel}\newcommand{\domain}[1]{\operatorname{Dom}(#1)} \newcommand{\range}[1]{\operatorname{Range}(#1)} \newcommand{\linearspan}{\operatorname{span}} \newcommand{\abs}[1]{\lvert #1 \rvert} \newcommand{\set}[2]{\left\{ #1 \: \middle\vert \: #2 \right\}} \renewcommand{\vec}[1]{\mathbf{#1}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \DeclareMathOperator{\Lapl}{\mathcal{L}} \newcommand{\La}[1]{\Lapl \left\{ #1 \right\}} \newcommand{\invLa}[1]{\Lapl^{-1}\left\{ #1 \right\}} \newcommand{\intbyparts}[4]{\begin{tabular}{|rl|rl|}\hline $u$ \amp $#1$ \amp $dv$ \amp $#2$ \\ \hline $du$ \amp $#3$ \amp $v$ \amp $#4$ \\ \hline \end{tabular}} \newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}} \newcommand{\notsubset}{\not\subset} \newcommand{\swap}{\mathrm{swap}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\half}{\text{ \nicefrac{1}{2}}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Section5.4Basis and Dimension

SubsectionBasis

Definition5.4.1

A basis for a vector space is a finite set of vectors that

  1. is linearly independent, and

  2. spans the vector space.

SubsectionDimension

Definition5.4.2

The dimension of a vector space, \(V\text{,}\) is the number of vectors in a basis for \(V\text{.}\)

SubsectionExercises

1

Place holder text.

Solution
2

Place holder text.

Solution
3

Place holder text.

Solution