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Question 1
61473

The matrix \(\left[ {\begin{array}{*{20}{c}}4&2\\1&1\end{array}} \right]\) maps the unit square to a parallelogram. Find the area of the parallelogram. 

\(2\,u^2\)

$$
\begin{array}{l}
{\left[\begin{array}{ll}
4 & 2 \\
1 & 1
\end{array}\right] \rightarrow \operatorname{det}\left[\begin{array}{ll}
4 & 2 \\
1 & 1
\end{array}\right]=4-2=2} \\
\therefore \text { Area of parallelogram }=2 \times 1
=2 u^{2}
\end{array}
$$

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