Question: Let

\[T\left( \begin{matrix} a \\ b \\ c \\ \end{matrix} \right)=\left( a+b \right)\left( \begin{matrix} 5 \\ 4 \\ \end{matrix} \right)+\left( b-2c-a \right)\left( \begin{matrix} 2 \\ -3 \\ \end{matrix} \right)+\left( 3a-5c \right)\left( \begin{matrix} -1 \\ 5 \\ \end{matrix} \right)\]

Find m and n where \(T:{{\mathbb{R}}^{n}}\to {{\mathbb{R}}^{m}}\), and the standard matrix of T. Is the linear transformation one-to-one, onto?