Dot Product

Problem Statement

Compute dot products and matrix multiplications.

Background

NumPy provides several multiplication operations:

• np.dot(a, b) - dot product
• a @ b - matrix multiplication (Python 3.5+)
• a * b - element-wise multiplication

For vectors: dot product = sum of element-wise products For matrices: standard matrix multiplication

Your Task

Write a function compute_products(vec1, vec2, mat) that computes various products.

Output Format

Return a dictionary with:

• "dot": Dot product of vec1 and vec2 (scalar)
• "elementwise": Element-wise product of vec1 and vec2 (list)
• "mat_vec": Matrix times vec1 (list)
• "vec_mat": vec1 times matrix (list)