1. The problem involves solving a system of linear equations and understanding a 2x2 matrix. 2. The system of equations is: $$x + ay = b$$ $$x + 2y = c$$ 3. To solve for $x$ and $y$, we can use substitution or elimination. Here, we use elimination: Subtract the second equation from the first: $$x + ay - (x + 2y) = b - c$$ Simplify: $$x + ay - x - 2y = b - c$$ $$ay - 2y = b - c$$ $$y(a - 2) = b - c$$ 4. Provided $a \neq 2$, solve for $y$: $$y = \frac{b - c}{a - 2}$$ 5. Substitute $y$ back into the second equation to find $x$: $$x + 2y = c$$ $$x = c - 2y = c - 2 \times \frac{b - c}{a - 2}$$ 6. The chemical equation given is: $$aNO_2 + bH_2O \rightarrow cHNO_2 + dHNO_3$$ with the relation: $$2a + b = 2c + 3d$$ This is a stoichiometric balance equation relating coefficients. 7. The matrix $A$ is: $$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ which is a 2x2 matrix with elements $a, b$ in the first row and $c, d$ in the second row. 8. The matrix order is 2x2, meaning 2 rows and 2 columns. Summary: - Solved for $y$ and $x$ in terms of $a, b, c$. - Noted the chemical equation balance. - Defined the matrix $A$ and its order. Final answers: $$y = \frac{b - c}{a - 2}$$ $$x = c - 2 \times \frac{b - c}{a - 2}$$