\[
\left(\begin{array}{lll}
* & b & * \\
a & * & * \\
* & * & c
\end{array}\right)
\]
a) A linear transformation \( \mathbf{R}^{3} \rightarrow \mathbf{R}^{3} \) maps \( (x, y, z)^{\top} \) to \( (2 x+5 y,-x+y+z, z)^{\top} \). What are the entries \( a, b \), and
Answers:
\[
\begin{array}{l}
\mathrm{a}=-1 \\
\mathrm{~b}=5 \\
\mathrm{c}=4
\end{array}
\]
b) If the linear transformation is the reflection through the origin of \( \mathbf{R}^{3} \), what are \( a, b \) and \( c \) ?
Answers:
\[
\begin{array}{l}
a=-1 \times \\
b=-5
\end{array}
\]
\[
c=1 \times
\]
