Array Broadcasting

Problem Statement

Perform element-wise operations between arrays of different shapes.

Background

Broadcasting rules:

1. Dimensions are compared from right to left
2. Dimensions are compatible if equal or one of them is 1
3. Arrays are "stretched" to match

Example: (3, 1) + (1, 4) → (3, 4)

Your Task

Write a function broadcast_arrays(row_vec, col_vec) that demonstrates broadcasting.

Given:

• row_vec: Shape (1, n) - a row vector
• col_vec: Shape (m, 1) - a column vector

Output Format

Return a dictionary with:

• "sum": row_vec + col_vec (broadcasts to m×n)
• "product": row_vec * col_vec (broadcasts to m×n)
• "result_shape": Shape of result (as list)