Solutions

DL-C01-C-001

A vector with 9 entries has one axis of length 9, so the shape is (9).

Rows come first and columns come second. A matrix with 7 rows and 4 columns has shape (7, 4).

The shape (32, 12) means 32 examples and 12 features per example. The batch size is 32.

The second dimension is the feature dimension, so each example has 12 features.

The product has shape:

(6, 5) x (5, 2) -> (6, 2)

The shared dimension 5 is used inside the product. The remaining dimensions are 6 and 2.

The product would require:

(6, 5) x (4, 2)

The inner dimensions are 5 and 4. They do not match, so the product is not valid.

The axis names are (batch, positions, features), and the shape is (3, 7, 16).

The feature axis is last, so each position has 16 features.

The first shape contains:

2 x 6 = 12

The second shape contains:

3 x 4 = 12

The entry count is preserved, so the reshape is valid.

The batch has shape (9, 5), and the bias has one value per feature.

The bias is reused for each of the 9 rows, so the output keeps shape (9, 5).

The layer accepts 12 input features and produces 6 output features.

In (input_features, output_features) order, the weight matrix has shape (12, 6).