# Deep Learning IIT Ropar Week 5 Nptel Answers

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## Table of Contents

## 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

**These are Deep Learning IIT Ropar Week 5 Nptel Assignment Answers**

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