The exam generally tests: > Python Programming > Basic ML Theory . MBZUAI Entry Exam Sample Questions Section 1: Linear Algebra (30%) Question 1: Let ( A ) be a 3x3 matrix with eigenvalues ( 2, -1, 3 ). What is the determinant of ( A^2 - 2A )?
Consider ( f(x) = x^3 - 2x + 1 ). Perform one iteration of gradient descent starting at ( x_0 = 1 ) with learning rate ( \eta = 0.1 ). What is ( x_1 )? mbzuai entry exam sample questions
Given vectors ( u = (1, 2, -1) ), ( v = (0, 1, 3) ). Compute the projection of ( u ) onto ( v ). The exam generally tests: > Python Programming >
def func(x, lst=[]): lst.append(x) return lst print(func(1)) print(func(2)) Write a Python function normalize(X) that takes a 2D numpy array X (samples × features) and returns a zero-mean, unit-variance normalized version (feature-wise). Do not use sklearn . Consider ( f(x) = x^3 - 2x + 1 )
What is the bias-variance decomposition of expected test error? Write the formula and briefly explain each term. Section 4: Machine Learning Basics (15%) Question 10: Why does L2 regularization produce smaller but non-zero weights, while L1 regularization can produce exact zeros?
Briefly explain how backpropagation computes gradients in a neural network. Why is the chain rule essential? Section 5: Python & Coding Logic (10%) Question 13: What is the output of the following?