Solutions

DL-C03-C-001

x . w + b = 2 x 5 + (-1) x 3 + 4
          = 10 - 3 + 4
          = 11

DL-C03-C-002

The bias is the constant term. In score = -2x_1 + 6x_2 - 9, the bias is -9.

DL-C03-C-003

A multiclass classifier produces one score per class. With 7 classes, it produces 7 scores for one example.

DL-C03-C-004

(20, 8) x (8, 3) -> (20, 3)

The bias has shape (3), so it broadcasts across the 20 examples. The score matrix has shape (20, 3).

DL-C03-C-005

score = 2x_1 - x_2 - 3
      = 2 x 4 - 5 - 3
      = 8 - 5 - 3
      = 0

The point is on the decision boundary.

DL-C03-C-006

A binary linear classifier has boundary x . w + b = 0. In two dimensions, that boundary is a line.