Linear Algebra Matrix operations & backprop

Shapes: X @ W + b produces predictions with the same shape as targets Y.

Learning: Each SGD step samples one example and updates W and b by subtracting learning_rate * gradient. The data stays fixed.

Comparisons: Learning-rate comparisons hold the initial weights, biases, and sampled examples fixed. Each comparison starts training from those same initial parameters.

Progress: loss_history records full-data MSE before training and after each of ten updates. Lower is better, but individual SGD steps can increase it.