Skip to main content
Contents Index Dark Mode Prev Up Next Scratch ActiveCode \(\newcommand{\identity}{\mathrm{id}}
\newcommand{\notdivide}{{\not{\mid}}}
\newcommand{\notsubset}{\not\subset}
\newcommand{\lcm}{\operatorname{lcm}}
\newcommand{\gf}{\operatorname{GF}}
\newcommand{\inn}{\operatorname{Inn}}
\newcommand{\aut}{\operatorname{Aut}}
\newcommand{\Hom}{\operatorname{Hom}}
\newcommand{\cis}{\operatorname{cis}}
\newcommand{\chr}{\operatorname{char}}
\newcommand{\Null}{\operatorname{Null}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\newcommand{\sfrac}[2]{{#1}/{#2}}
\)
Exercises 5.12 Matching Exercises
Matching exercises come in two varieties. Their differences are most noticeable in interactive versions.
Cardsort
A
<cardsort> asks users to match items in a 1-1 or many-1 fashion. The interactive version of these involves dragging “card”s from the left column (the
<premise>s) into containers on the right (the
<response>s).
Matching
A
<matching> interactive asks users to form connections between the
<premise>s in the left column and the
<response>s on the right. This format supports many-many matches.
1. Cardsort Problem, Dates.
Match each event in United States history with the year it happened.
Monroe Doctrine
1823
Haymarket Riot
1886
Louisiana Purchase
1803
Battle of Gettysburg
1863
2. Cardsort Problem, Derivatives.
3. Cardsort Problem, Linear Algebra.
Match each subspace with a basis for that subspace. (You may assume that each set is really a basis for at least one of the subspaces.)
Each putative basis is a subset of exactly one of the three subspaces. So for each subspace, two of the three sets can be ruled out by simply testing that the vectors of the basis are members of the subspace, via the membership criteria.
\(\left\{\langle x,y,z\rangle\mid - y + z = 0\right\}\) \(\left\{\langle -4, 3, 3\rangle, \langle 3, -2, -2 \rangle\right\}\) \(\left\{\langle x,y,z\rangle\mid -3x - 5y + z = 0\right\}\) \(\left\{\langle -4, 3, 3\rangle, \langle 5, -4, -5 \rangle\right\}\) \(\left\{\langle x,y,z\rangle\mid -2x - 5y + 2z = 0\right\}\) \(\left\{\langle 3, -2, -2 \rangle, \langle 5, -4, -5 \rangle\right\}\) Hint .
For openers, a basis for a subspace must be a
subset of the subspace.
4. Cardsort Problem, Function Types.
Sort the following functions into their correct categories.
\(y=5x+3\) \(\pi x - 6y = \sqrt{2}\) \(y=\frac{-1}{2}x+e\) Linear
Quadratic
\(y=x^3-x\) \(y=2^x\) Exponential
\(y=x^3\) \(y=\sqrt{x}\) Power
5. Matching Problem, Playing Cards.
6. Matching Problem, Popular Music History.
