A = (1 2 / 0 1) B = (3 1 / 2 0) find 2A + B. C = (2 −3 / 0 4) and D = (5 −2 / -7 1) Express as a Single matrics D2. F = (3 2 / -4 -6) g = (3 −2 / 2 -1) and H = (7 / 1) find GH. M = (8 −4 / -5 3) and N = (1 / 3) find MN

$$2A + B = \begin{pmatrix} 2 & 4 \\ 0 & 2 \end{pmatrix} + \begin{pmatrix} 3 & 1 \\ 2 & 0 \end{pmatrix} = \begin{pmatrix} 2+3 & 4+1 \\ 0+2 & 2+0 \end{pmatrix} = \begin{pmatrix} 5 & 5 \\ 2 & 2 \end{pmatrix}$$

The result is:

$$\boxed{\begin{pmatrix} 5 & 5 \\ 2 & 2 \end{pmatrix}}$$

2) Express $D^2$ as a single matrix
Given $D = \begin{pmatrix} 5 & -2 \\ -7 & 1 \end{pmatrix}$.

$$D^2 = \begin{pmatrix} 5 & -2 \\ -7 & 1 \end{pmatrix} \begin{pmatrix} 5 & -2 \\ -7 & 1 \end{pmatrix}$$ $$D^2 = \begin{pmatrix} (5)(5) + (-2)(-7) & (5)(-2) + (-2)(1) \\ (-7)(5) + (1)(-7) & (-7)(-2) + (1)(1) \end{pmatrix}$$ $$D^2 = \begin{pmatrix} 25 + 14 & -10 - 2 \\ -35 - 7 & 14 + 1 \end{pmatrix}$$ $$D^2 = \begin{pmatrix} 39 & -12 \\ -42 & 15 \end{pmatrix}$$

The result is:

$$\boxed{\begin{pmatrix} 39 & -12 \\ -42 & 15 \end{pmatrix}}$$

3) Find $GH$
Given $G = \begin{pmatrix} 3 & -2 \\ 2 & -1 \end{pmatrix}$ and $H = \begin{pmatrix} 7 \\ 1 \end{pmatrix}$.

$$GH = \begin{pmatrix} 3 & -2 \\ 2 & -1 \end{pmatrix} \begin{pmatrix} 7 \\ 1 \end{pmatrix}$$ $$GH = \begin{pmatrix} (3)(7) + (-2)(1) \\ (2)(7) + (-1)(1) \end{pmatrix}$$ $$GH = \begin{pmatrix} 21 - 2 \\ 14 - 1 \end{pmatrix}$$ $$GH = \begin{pmatrix} 19 \\ 13 \end{pmatrix}$$

The result is:

$$\boxed{\begin{pmatrix} 19 \\ 13 \end{pmatrix}}$$

4) Find $MN$
Given $M = \begin{pmatrix} 8 & -4 \\ -5 & 3 \end{pmatrix}$ and $N = \begin{pmatrix} 1 \\ 3 \end{pmatrix}$.

$$MN = \begin{pmatrix} 8 & -4 \\ -5 & 3 \end{pmatrix} \begin{pmatrix} 1 \\ 3 \end{pmatrix}$$ $$MN = \begin{pmatrix} (8)(1) + (-4)(3) \\ (-5)(1) + (3)(3) \end{pmatrix}$$ $$MN = \begin{pmatrix} 8 - 12 \\ -5 + 9 \end{pmatrix}$$ $$MN = \begin{pmatrix} -4 \\ 4 \end{pmatrix}$$

The result is:

$$\boxed{\begin{pmatrix} -4 \\ 4 \end{pmatrix}}$$