deep laurel
I am currently working on a linear algebra problem and I am having trouble with some parts of it. The problem involves using matrices to represent linear transformations. The matrices given are:
$$
A=\left[\begin{array}{ll}
1 & 0 \
1 & 1
\end{array}\right], \quad B=\left[\begin{array}{cc}
0 & 1 \
-1 & 0
\end{array}\right]
$$
The problem has several parts, and I am unsure about the first three:
\begin{enumerate}
\item (a) Draw a figure showing how the two base vectors $\mathbf{e}{x}=\left[\begin{array}{l}1 \ 0\end{array}\right]$ and $\mathbf{e}{y}=\left[\begin{array}{l}0 \ 1\end{array}\right]$ are transformed by the matrix $A$.
\item (b) Draw a figure showing how $\mathbf{e}{x}$ and $\mathbf{e}{y}$ are transformed by the matrix $B$.
\item (c) A composite transformation can be created by combining two transformations. Here, we will study the composite transformation obtained if we first create the transformation $\mathbf{u} \rightarrow A \mathbf{u} \equiv \mathbf{v}$, and then create the transformation $\mathbf{v} \rightarrow B \mathbf{v}=B(A \mathbf{u})$. Draw a figure showing the image of the composite transformation for $\mathbf{u}=\mathbf{e}{x}$ and for $\mathbf{u}=\mathbf{e}{y}$.
\end{enumerate}
vivid obsidian
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