https://piazza.com/class_profile/get_resource/ln18bjs43q41tr/los7kh0sq2r55u

$$ 2x_1-x_2-6 = 0\\ x_2 = 2x_1 - 6\\ $$

a) Definitely true: if converges, data must be linearly separable

b) Definitely true: if converges, data must be linearly separable, and therefore it will converge again regardless of the permutation

c) Possibly false: even if data is linearly separable and it will converge, it may take longer than k steps to converge or shorter based on the permutation

d) Possibly false: k can be greater than n in instances where the algorithm may take multiple passes over the dataset to find a separating hyperplane, especially if the data points are close to the decision boundary or if the initial weight values are not optimal.

b = q - p

$$ w = [3, 4]\\ b = -12 \\ w * x + b = [3, 4] \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} - 12 \\

= 3x_1 + 4x_2 - 12 \\ x_2 = \frac{-3x_1+12}{4}\\ $$

a) b)

c)

$$ ||w|| = \sqrt{3^2 + 4^2}\\ = \sqrt{9+ 16} = 5 \\ M = 2 * \frac{1}{5}

$$

d)