Question

$\implies \sf \: X + Y + X - Y = \begin{bmatrix} \sf \: 1& \sf \: 2 \\ \sf \: 1& \sf \: 1 \end{bmatrix} + \begin{bmatrix} \sf \: 3& \sf \: 0 \\ \sf \: - 1& \sf \: 1 \end{bmatrix} \\ \\ \\ \implies \sf \:2X = \begin{bmatrix} \sf \: 1 + 3& \sf \: 2 + 0\\ \sf \: 1 - 1& \sf \: 1 + 1 \end{bmatrix} \\ \\ \\ \implies \sf \:2X = \begin{bmatrix} \sf \: 4& \sf \: 2 \\ \sf \: 0& \sf \: 2\end{bmatrix} \\ \\ \\ \implies \sf \: X = \begin{bmatrix} \sf \: \frac{4}{2} & \sf \: \frac{2}{2} \\ \\ \sf \: \frac{0}{2} & \sf \: \frac{2}{2} \end{bmatrix} \\ \\ \\ \sf \implies \blue{X = \begin{bmatrix} \sf \: 2& \sf \: 1 \\ \sf \: 0& \sf \: 1\end{bmatrix}}$
Substitute the value of X in equation (1).

$\implies \sf \: \begin{bmatrix} \sf \: 2& \sf \: 1 \\ \sf \: 0& \sf \: 1\end{bmatrix} + Y = \begin{bmatrix} \sf \: 1& \sf \: 2 \\ \sf \: 1& \sf \: 1 \end{bmatrix} \\ \\ \\ \implies \sf \:Y = \begin{bmatrix} \sf \: 1& \sf \: 2 \\ \sf \: 1& \sf \: 1 \end{bmatrix} - \begin{bmatrix} \sf \: 2& \sf \: 1 \\ \sf \: 0& \sf \: 1\end{bmatrix} \\ \\ \\ \implies \sf \:Y =\begin{bmatrix} \sf \: 1 - 2& \sf \: 2 - 1 \\ \sf \: 1 - 0& \sf \: 1 - 1 \end{bmatrix} \\ \\ \\ \implies \sf \blue{ \:Y =\begin{bmatrix} \sf \: - 1 & \sf \: 1 \\ \sf \: 1 & \sf \: 0 \end{bmatrix}}$​

Answer 1

Answer:

a system of government by the whole population or all the eligible members of a state, typically through elected representatives.

Answer 2

$\implies \sf \: \begin{bmatrix} \sf \: 2& \sf \: 1 \\ \sf \: 0& \sf \: 1\end{bmatrix} + Y = \begin{bmatrix} \sf \: 1& \sf \: 2 \\ \sf \: 1& \sf \: 1 \end{bmatrix} \\ \\ \\ \implies \sf \:Y = \begin{bmatrix} \sf \: 1& \sf \: 2 \\ \sf \: 1& \sf \: 1 \end{bmatrix} - \begin{bmatrix} \sf \: 2& \sf \: 1 \\ \sf \: 0& \sf \: 1\end{bmatrix} \\ \\ \\ \implies \sf \:Y =\begin{bmatrix} \sf \: 1 - 2& \sf \: 2 - 1 \\ \sf \: 1 - 0& \sf \: 1 - 1 \end{bmatrix} \\ \\ \\ \implies \sf \blue{ \:Y =\begin{bmatrix} \sf \: - 1 & \sf \: 1 \\ \sf \: 1 & \sf \: 0 \end{bmatrix}}$