Deep Learning IIT Ropar Week 5 Nptel Answers
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Deep Learning IIT Ropar Week 5 Nptel Assignment Answers (July-Dec 2024)
1. Which of the following is a measure of the amount of variance explained by a principal component in PCA?
a) Covariance
b) Correlation
c) Mean absolute deviation
d) Eigenvalue
Answer: d) Eigenvalue
2. What is/are the limitations of PCA?
a) It is computationally less efficient than autoencoders
b) It can only reduce the dimensionality of a dataset by a fixed amount.
c) It can only identify linear relationships in the data.
d) It can be sensitive to outliers in the data.
Answer: d) It can be sensitive to outliers in the data.
3. Which of the following is a property of eigenvalues of a symmetric matrix?
a) Eigenvalues are always positive
b) Eigenvalues are always negative
c) Eigenvalues are always real
d) Eigenvalues can be complex numbers with imaginary parts non-zero
Answer: c) Eigenvalues are always real
4. The eigenvalues of A are 3, 4. Which of the following are the eigenvalues of A³?
a) 3, 4
b) 9, 16
c) 27, 64
d) √3, √4
Answer: b) 9, 16
5. If we have a 12×12 matrix having entries from R, how many linearly independent eigenvectors corresponding to real eigenvalues are possible for this matrix?
a) 10
b) 24
c) 12
d) 6
Answer: c) 12
6. What is the mean of the given data points x₁, x₂, x₃?
a) [5.5]
b) [1.67, 1.67]
c) [2.2]
d) [1.5, 1.5]
Answer: b) [1.67, 1.67]
7. The covariance matrix C=1/n ∑(x−x̄)(x−x̄)T is given by:
a) [0.22, −0.11; −0.11, 0.22]
b) [0.33, −0.17; −0.17, 0.33]
c) [0.22, −0.22; −0.22, 0.22]
d) [0.33, −0.33; −0.33, 0.33]
Answer: a) [0.22, −0.11; −0.11, 0.22]
8. The maximum eigenvalue of the covariance matrix C is:
a) 0.33
b) 0.67
c) 1
d) 0.5
Answer: d) 0.5
9. The eigenvector corresponding to the maximum eigenvalue of the given matrix C is:
a) [0.71, 0.71]
b) [−0.71, 0.71]
c) [−1, 1]
d) [1, 1]
Answer: a) [0.71, 0.71]
10. What is the determinant of a 2×2 matrix that has eigenvalues of 4 and 5?
Answer: 20
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