ML CodingeasyNumpy~10m

Matrix Product

Problem

You are implementing a forward pass in a neural network. At the core of every dense layer is a matrix multiplication — the input activations matrix multiplied by the weight matrix produces the layer output.

Given two 2D matrices A (shape m×n) and B (shape n×p), return their matrix product A @ B as a list of lists.

The result will have shape (m, p) where result[i][j] = sum of A[i][k] * B[k][j] for k in range(n).

Examples

Example 1

Input: ([[1, 2, 3], [4, 5, 6]], [[1, 0], [0, 1], [1, 1]])

Output: [[4, 5], [10, 11]]

2×3 @ 3×2 = 2×2. Row 0: [11+20+31, 10+21+31] = [4, 5]. Row 1: [4+0+6, 0+5+6] = [10, 11].

Example 2

Input: ([[1], [2], [3]], [[4, 5, 6]])

Output: [[4, 5, 6], [8, 10, 12], [12, 15, 18]]

3×1 @ 1×3 = 3×3 outer product. Each row i is scaled by A[i][0].

Example 3

Input: ([[1, 1], [0, 1]], [[1, 0], [1, 1]])

Output: [[2, 1], [1, 1]]

Order matters — A@B ≠ B@A. B@A would give [[1,1],[1,2]].

Constraints

›1 <= m, n, p <= 50
›-100 <= A[i][j], B[i][j] <= 100
›A has shape (m, n), B has shape (n, p)

Reference solution

Reference solution available after you attempt the question.

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