$\newenvironment {prompt}{}{} \newcommand {\DeclareMathOperator }{\@OldDeclareMathOperator {##1}{##2}\immediate \write \myfile {\unexpanded {\DeclareMathOperator }{\unexpanded {##1}}{\unexpanded {##2}}}} \newcommand {\amatrix }{\left [\begin {array}{@{}*{##1}{c}|c@{}} } \newcommand {\RR }{\bf R} \newcommand {\adj }{\mathop {\rm adj}} \newcommand {\degrees }{^{\circ }} \newcommand {\Col }{\mathop {\rm Col}} \newcommand {\diag }{\mathop {\rm diag}} \newcommand {\Inn }{\mathop {\rm Inn}} \newcommand {\Nul }{\mathop {\rm Nul}} \newcommand {\rank }{\mathop {\rm rank}} \newcommand {\rk }{\mathop {\rm rk}} \newcommand {\Row }{\mathop {\rm Row}} \newcommand {\Span }{\mathop {\rm Span}} \newcommand {\spec }{\mathop {\rm spec}} \newcommand {\tr }{\mathop {\rm tr}} \newcommand {\vol }{\mathop {\rm vol}} \newcommand {\reserved@a }{} \newcommand {\reserved@a }{} \newcommand {\HyperFirstAtBeginDocument }{\AtBeginDocument } \newcommand {\reserved@a }{} \newcommand {\reserved@a }{} \newcommand {\AppendGraphicsExtensions }{\@ifundefined {Gin@extensions}{\let \Gin@extensions \@empty }{}\@ifstar {\grfext@Append \grfext@Check }{\grfext@Append \grfext@@Add }} \newcommand {\PrependGraphicsExtensions }{\@ifundefined {Gin@extensions}{\let \Gin@extensions \@empty }{}\@ifstar {\grfext@Prepend \grfext@Check }{\grfext@Prepend \grfext@@Add }} \newcommand {\RemoveGraphicsExtensions }{\@ifundefined {Gin@extensions}{\def \Gin@extensions {}}{\edef \grfext@tmp {\zap@space ##1 \@empty }\@for \grfext@ext :=\grfext@tmp \do {\def \grfext@next {\let \grfext@tmp \Gin@extensions \@expandtwoargs \@removeelement \grfext@ext \Gin@extensions \Gin@extensions \ifx \grfext@tmp \Gin@extensions \let \grfext@next \relax \fi \grfext@next }\grfext@next }}\grfext@Print \RemoveGraphicsExtensions } \newcommand {\epstopdfsetup }{\setkeys {ETE}} \newcommand {\epstopdfcall }{\ifETE@InsideSetfile \expandafter \@firstoftwo \else \expandafter \@secondoftwo \fi {‘##1}{\Gin@base \Gin@ext }} \newcommand {\epstopdfDeclareGraphicsRule }{\ifx \\##4\\\@PackageError {epstopdf-base}{Conversion command is missing}\@ehc \else \begingroup \@ifundefined {Gin@rule@##1}{}{\@PackageInfo {epstopdf-base}{Redefining graphics rule for ‘##1’}}\endgroup \@namedef {Gin@rule@##1}####1{{##2}{##3}{\epstopdfcall {##4}}}\fi } \newcommand {\mdf@patchamsthm }{\let \mdf@deferred@thm@head \deferred@thm@head \pretocmd {\deferred@thm@head }{\@inlabelfalse }{\mdf@PackageInfo {mdframed detected package amsthm changed the theorem header of amsthm\MessageBreak }}{\mdf@PackageError {mdframed detected package amsthm changed the theorem header of amsthm failed\MessageBreak }}} \newcommand {\GetTitleStringSetup }{\setkeys {gettitlestring}} \newcommand {\GetTitleString }{\ifGTS@expand \expandafter \GetTitleStringExpand \else \expandafter \GetTitleStringNonExpand \fi } \newcommand {\GetTitleStringExpand }{\def \GetTitleStringResult {##1}\begingroup \GTS@DisablePredefinedCmds \GTS@DisableHook \edef \x {\endgroup \noexpand \def \noexpand \GetTitleStringResult {\GetTitleStringResult }}\x } \newcommand {\GetTitleStringNonExpand }{\def \GetTitleStringResult {##1}\global \let \GTS@GlobalString \GetTitleStringResult \begingroup \GTS@RemoveLeft \GTS@RemoveRight \endgroup \let \GetTitleStringResult \GTS@GlobalString } \newcommand {\GTS@DisableHook }{} \newcommand {\label@hook }{} \newcommand {\@currentlabelname }{} \newcommand {\reserved@a }{} \newcommand {\@safe@activestrue }{} \newcommand {\@safe@activesfalse }{} \newcommand {\nameref }{\@ifstar \T@nameref \T@nameref } \newcommand {\Sectionformat }{##1} \newcommand {\vnameref }{\unskip ~\nameref {##1}\@vpageref [\unskip ]{##1}} \newcommand {\ref }{\@ifstar \@refstar \T@ref } \newcommand {\pageref }{\@ifstar \@pagerefstar \T@pageref } \newcommand {\nameref }{\@ifstar \@namerefstar \T@nameref } \newcommand {\reserved@a }{} \newcommand {\reserved@a }{} \newcommand {\reserved@a }{\AtBeginDocument } \newcommand {\reserved@a }{} \newcommand {\reserved@a }{}$
True/False: $$ matrices $$ and $$ are said to be similar if $$ for some invertible matrix $$.
True False
Let $$ and let $$. What is $$?
$$ $$ $$ $$

Let $$ and let $$. What is $$?
$$ $$ $$ $$

Let $$ such that $$ and $$. Compute the following:

$$

$$

True/False: An $$ matrix $$ is diagonalizable if and only if $$ has exactly $$ eigenvectors.
True False
True/False: If a $$ matrix $$ has a linearly independent set of four eigenvectors, then $$ is diagonalizable.
True/False: It is possible for an $$ matrix $$ to have a linearly independent set of more than $$ eigenvectors.
$$ has $$ eigenvalues (counting multiplicities). For each eigenvalue, the eigenspace has dimension less than or equal to the multiplicity of the eigenvalue.