Is anyone able to help me do the following proof please:
Let f:R3 > R3 be given by
f(x1,x2,x3)=(x3,x1+x2,x1-x2)
Prove that f is a linear transformation.
Many thanks to anyone who can help.
Hi
You have to prove two things :
- For all $\displaystyle x=\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix},\,y=\b egin{pmatrix}y_1\\y_2\\y_3\end{pmatrix} \in \mathbb{R}^3$, $\displaystyle f(x+y)=f(x)+f(y)$
- For all $\displaystyle \lambda \in \mathbb{R}, \,x=\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}\in\m athbb{R}^3$, $\displaystyle f(\lambda x)=\lambda f(x)$