Firstly, to multiply \mathbf{a} by 2, we must multiply both of its components by 2:

2\mathbf{a}=2\times\begin{pmatrix}3\\8\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}

Then, to add this to \mathbf{b}, we must add the x values and y values separately. Doing so, we get the answer to be:

2\mathbf{a}+\mathbf{b}=\begin{pmatrix}6\\16\end{pmatrix}+\begin{pmatrix}-7\\2\end{pmatrix}=\begin{pmatrix}-1\\18\end{pmatrix}

Firstly, to multiply \mathbf{a} by 3, we must multiply both of its components:

3\mathbf{a}=3\times\begin{pmatrix}2\\7\end{pmatrix}=\begin{pmatrix}6\\21\end{pmatrix}

Then, in order subtract 2\mathbf{b}, we must first multiply \mathbf{b} by 2.

2\mathbf{b}=2\times\begin{pmatrix}-5\\3\end{pmatrix}=\begin{pmatrix}-10\\6\end{pmatrix}

Thus the calculation is:

3\mathbf{a}-2\mathbf{b}=\begin{pmatrix}6\\21\end{pmatrix}-\begin{pmatrix}-10\\6\end{pmatrix}=\begin{pmatrix}16\\15\end{pmatrix}

Firstly, to multiply \mathbf{b} by 2, we must multiply both of its components:

2\mathbf{b}=2\times\begin{pmatrix}5\\-3\end{pmatrix}=\begin{pmatrix}10\\-6\end{pmatrix}

Then, we can add \mathbf{a}  and  2\mathbf{b}:

\mathbf{a}+2\mathbf{b}=\begin{pmatrix}6\\2\end{pmatrix}+\begin{pmatrix}10\\-6\end{pmatrix}=\begin{pmatrix}16\\-4\end{pmatrix}

The final calculation is to subtract \mathbf{c}:

\mathbf{a}+2\mathbf{b}-\mathbf{c}=\begin{pmatrix}16\\-4\end{pmatrix}-\begin{pmatrix}2\\1\end{pmatrix} = \begin{pmatrix}14\\-5\end{pmatrix}