1. The problem asks to find the value of $x$ for which the matrix $\begin{bmatrix} 2 & 4 \end{bmatrix}$ is singular. However, this is a 1x2 matrix (a row vector), and singularity is defined for square matrices only. So, this part is not applicable. 2. Next, we analyze the graph with a line passing through points $(0,11)$ and $(6,0)$. 3. To find the gradient (slope) of the line, use the formula: $$\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1) = (0,11)$ and $(x_2,y_2) = (6,0)$. 4. Calculate the slope: $$m = \frac{0 - 11}{6 - 0} = \frac{-11}{6}$$ 5. The gradient of the line is $-\frac{11}{6}$. 6. To find the equation of the line, use the point-slope form: $$y - y_1 = m(x - x_1)$$ Substitute $m = -\frac{11}{6}$ and point $(0,11)$: $$y - 11 = -\frac{11}{6}(x - 0)$$ 7. Simplify the equation: $$y = 11 - \frac{11}{6}x$$ 8. This is the equation of the line in slope-intercept form. Final answers: (i) Gradient of the line: $-\frac{11}{6}$ (ii) Equation of the line: $y = 11 - \frac{11}{6}x$