Quiz Space

Machine Learning Foundations · Quiz 2 · 23 Nov 2025 · September 2025 term

Question 17: The data-points\ and\ are added to\ to get\ . PCA is run…

Question 17

+2 marksOne correct option

Based on the above data, answer the given subquestions.

The data-points
and
are added to
to get
. PCA is run on . The

covariance matrix of
is
and the unit-norm eigenvector corresponding to the largest

eigenvalue of
is
. Which of the following is true?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
See the whole paperTake it as a mock test

Question 17 of 17 in the IIT Madras BS Machine Learning Foundations (MLF) Quiz 2 paper sat on 23 Nov 2025, in the September 2025 term (IIT M DIPLOMA AN EXAM QDD2 23 Nov 2025 NEW). It carries 2 marks.

More questions from this paper

  1. Q1Consider the quadratic form\ . If , where\ and\ is a\ matrix, which of the following is ?
  2. Q2Figure question
  3. Q3Consider a matrix\ of shape\ . The SVD of\ is given by\ . The columns of are the left singular vectors and the columns …
  4. Q4Suppose\ . What is the value of\ when\ is minimum?
  5. Q5For each sub-question, answer whether it is true or false. The singular value decomposition exists only for square matr…
  6. Q6For each sub-question, answer whether it is true or false. If\ is Hermitian, then eigenvectors corresponding to distinc…
  7. Q7Consider a unitary matrix\ as given below: Also,\ and\ .\ Based on the above data, answer the given subquestions. Enter…
  8. Q8Consider a unitary matrix\ as given below: Also,\ and\ .\ Based on the above data, answer the given subquestions. Enter…
  9. Q9Consider a unitary matrix\ as given below: Also,\ and\ .\ Based on the above data, answer the given subquestions.
  10. Q10Which of the following are the singular values of\ ?
  11. Q11If\ is a symmetric matrix, consider statements P and Q. •\ P: If\ is an eigenvalue of\ , then\ is a singular value of\ …
  12. Q12Starting at\ , run two steps of gradient descent with learning rate\ to obtain . If\ , enter the value of\ correct to t…
  13. Q13For what value of\ will gradient descent reach the minimum after exactly one step? Enter your answer correct to one dec…
  14. Q14Gradient descent is said to converge to the minimum p^ = (x^, y^), if the point p_t = (x_t, y_t) gets increasingly clos…
  15. Q15If the covariance matrix of the dataset is\ , find\ .
  16. Q16If the unit-norm eigenvector corresponding to the largest eigenvalue of\ is\ , find\ .