Deep Learning – IIT Ropar Week 5 Assignment Answers
Deep Learning – IIT Ropar Week 5 Assignment Answers (Jan-Apr 2026)
1. Which property of matrix M makes it suitable for modeling user transitions?
- It is diagonal and simplifies computation
- Each row sums to zero, ensuring conservation
- It preserves probability distributions across categories
- It contains distinct eigenvalues for each genre
Answer : c
2. What can be inferred about the dominant eigenvalue of matrix M?
- It is greater than 1 due to amplification effects
- It is equal to 1 as total probability is conserved
- It is negative because probabilities decay
- It varies depending on the initial user distribution
Answer : b
3. If the platform repeatedly applies the transformation vk+1=Mvk, what will eventually happen?
- User distribution oscillates indefinitely
- Users permanently concentrate in one genre
- The distribution converges to a steady state
- The magnitude of the vector increases over time
Answer : c
4. If the initial distribution of users is changed, will the final long-term distribution also change?
- Yes, early preferences permanently bias the outcome
- No, long-term behavior depends only on the transition model
- Only if the matrix is symmetric
- Only if complex eigenvalues are present
Answer : b
5. In this scenario, what does the dominant eigenvector of matrix M represent?
- A temporary surge in content popularity
- The genre with the fastest short-term growth
- The long-term proportion of users in each genre
- A randomly selected direction in vector space
Answer : c
6. What are the eigenvalues of matrix A?
- 0.7 and 0.4
- 1 and 0
- −0.7 and −0.4
- 0.28 and 0.16
Answer : a
7. What happens to the sequence xk=Akx0 as k→∞?
- It grows without bound
- It oscillates between fixed values
- It converges to the zero vector
- It stabilizes at a non-zero constant
Answer : c
8. Which sensor signal diminishes more rapidly over time?
- The first signal due to higher attenuation
- The second signal due to faster decay
- Both signals decay at the same rate
- The decay rate cannot be determined
Answer : b
9. What does this behavior indicate about the long-term system response?
- Signals continuously amplify
- Noise dominates and destabilizes the system
- Signals gradually stabilize and fade
- The system becomes chaotic over time
Answer : c
10. If one eigenvalue of matrix A were greater than 1, what would be the consequence?
- The system output becomes constant
- Signal values grow exponentially in that direction
- All signal components eventually vanish
- Eigenvectors no longer exist
Answer : b
11. What is the fundamental mathematical operation underlying PCA?
- Iterative gradient optimization
- Eigen-decomposition of the covariance matrix
- Random sampling of feature subsets
- Simple feature normalization
Answer : b
12. Why are principal components orthogonal to each other?
- To reduce computational complexity
- To increase feature correlation
- Due to properties of symmetric covariance matrices
- To preserve original data scale
Answer : c
13. Which principal components are typically removed during dimensionality reduction?
- Components with high variance
- Components with large eigenvalues
- Components with low variance
- Components closest to the mean
Answer : c
14. What does a principal component represent?
- A single observed feature
- A nonlinear transformation of inputs
- A linear combination of original features
- An average behavior pattern
Answer : c
15. While applying dimensionality reduction on the student activity dataset, the analytics team decides to use Singular Value Decomposition (SVD) directly on the data matrix instead of computing the covariance matrix first. What is the primary advantage of this approach?
- SVD ensures that all transformed features become statistically independent
- SVD can be applied effectively even when the no. of features exceeds the samples
- SVD automatically removes noise without selecting components
- SVD converts nonlinear relationships into linear representations
Answer : b