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Homework Statement
Which of the following functions is linear? Give reasons if they are not linear. If they are linear, give the corresponding matrix.
Homework Equations
a) [itex]
R
\begin{pmatrix}
x\\
y\\
\end{pmatrix} =
\begin{pmatrix}
x - y \\
x\\
\end{pmatrix}
[/itex]
b) [itex]
S
\begin{pmatrix}
a\\
b\\
\end{pmatrix} =
\begin{pmatrix}
5 \\
b\\
\end{pmatrix}
[/itex]
c) [itex]T(x \textbf{i} + y \textbf{j} + z \textbf{k}) = 6x \textbf{i} + y \textbf{j} - y \textbf{k} [/itex]
d)[itex]
U
\begin{pmatrix}
x\\
y\\
z\\
\end{pmatrix} =
\begin{pmatrix}
xy \\
y\\
z\\
\end{pmatrix}
[/itex]
The Attempt at a Solution
I have no idea how to do this question, I've tried to find some advice online and neither my notes nor the resources seem to help me.
Could someone possibly tell me what I'm supposed to do please?
Thanks