Skip to main content\(\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}
\newcommand{\diff}{\text{d}}
\newcommand{\mb}[1]{\mathbf{#1}}
\newcommand{\coord}[2]{[#1]^{#2}}
\newcommand{\chart}[2]{[#1]_{#2}}
\newcommand{\twovec}[2]{\left[ \begin{matrix} #1 \\ #2 \end{matrix} \right]}
\newcommand{\threevec}[3]{\left[ \begin{matrix} #1 \\ #2 \\ #3 \end{matrix} \right]}
\newcommand{\im}{{\text{im}}}
\newcommand{\cob}[3]{[#1]^{#3}_{#2}}
\newcommand{\rk}{\textnormal{rank}}
\newcommand{\nullity}{\textnormal{nullity}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 3 Linear Geometry
