Q1. Scenario: You have a 2D array of shape (3,4) representing batch features. You want to subtract the mean of each feature (column) and divide by standard deviation. Write the broadcasting code.
data = np.random.rand(3,4); mean = data.mean(axis=0); std = data.std(axis=0); normalized = (data - mean) / std. Broadcasting aligns (3,4) with (4,) and applies operation to each row. No loops needed.
Q2. Scenario: Add a constant bias term to each element of a 5x5 matrix. Show two ways: using broadcasting and using np.full.
arr = np.ones((5,5)); bias = 0.5; result1 = arr + bias; result2 = arr + np.full((5,5), bias). Both give 1.5 everywhere. Broadcasting automatically expands scalar to array shape.
Q3. Scenario: Multiply a 3x1 column vector by a 1x4 row vector. What shape is the result? Write code to produce the outer product.
col = np.array([[1],[2],[3]]); row = np.array([[10,20,30,40]]); result = col * row; shape (3,4). This is broadcasting: (3,1) * (1,4) -> (3,4). This is efficient for outer product. Equivalent to np.outer(col.flatten(), row.flatten()).
Q4. Scenario: You have an array of shape (2,3) and you want to add a 1D array of shape (3,) to each row. Write the code and explain broadcasting rules.
A = np.arange(6).reshape(2,3); b = np.array([10,20,30]); C = A + b. Shapes: (2,3) and (3,) -> (2,3). b is stretched to (2,3) implicitly. This adds b to each row. Works because trailing dimensions match.
Q5. Scenario: Create a 1D array of 5 numbers. Use broadcasting to compare it with a scalar threshold, producing a boolean array. Then use that boolean array to index the original array.
arr = np.array([2,5,1,8,3]); threshold = 4; mask = arr > threshold; result = arr[mask]; output: [5,8]. Broadcasting scalar to array, then boolean indexing. Useful for thresholding predictions.