This article provides you the answers for Week 2 Assignment of NPTEL Data Science for Engineers. The answers provided here are for free and all are verified with solutions. In the Previous article, we discussed about the Week 1 answers, the link is provided below.  If any change in the answers, please join in the telegram link provided below. 

Also Read: NPTEL Data Science for Engineers Week 1 Answers 2025 

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NPTEL Data Science for Engineers Week 2 Assignment 2025

In this Week, the NPTEL Lectures discussed about the various topics: 

• Linear Algebra
• Solving Linear Equations
• Distance, Hyperplanes
• Eigen Values
• Eigen Vectors

Last Date : 05-02-2025 

Q1. Are the Vectors are linearly Independent ? 

Options: 

      a. Yes

      b. No

Answer: [ B ] No

Solution: 

Q2. Does the set, S = (1,1), (1,2) spans R^2 ? 

Options: 

      a. Yes 

      b. No 

Answer: [ A ] Yes

Solution: 

Q3. Consider the following system of linear equations of the form Ax=b: 

       2x -3y+6z = 14

       x+y-2z = -3  

which among the following are correct ? 

Answer: [ A ] [ D ] 

Solution: 

Consider the following system of linear equation 

      x+y+z = -2 

      x+2y-z = 1 

      2x + ay + bz = 2 

Q4. Find the Conditions for a and b for which the above system has no solution. 

Options: 

    

Answer: [ B ] 

Solution: 

Q5.  Find Conditions on a and b for which the above system has a unique solution. 

Options: 

Answer: [ D ] 

Solution: 

Q6. Find Conditions on a and b for which the above system has a infinite number of Solutions. 

Options: 

Answer: [ C ] 

Solution: 

In solving the system Ax=b in the variables x1, x2, x3 and Gaussian Elimination on the Augmented matrix  [ A ] [ B ] led to the following row echelon form. 

 

Q7.  Identify the number of free variable from above row echelon matrix. 

Options: 

      A. 0 

      B. 1 

      C. 2

      D. 3 

Answer: [ B ] 1

Solution: 

Q8. Which among the following is correct for the above system Ax = b ? 

 Options: 

      A. It has infinite number of solutions 

      B. It has a unique solutions

      C. It has no solution 

Answer: [ A ] 

Q9.  For what values of a are matrix A  =  [   a     1   ]   not invertible 

                                                                        [ -2   a+3 ]   

   

 Options: 

       A. a = 1 

       B. a = -2 

       C. a = -1
       D. a = 2

Answer: [ B ] [ C ] 

Solution:  

Q10. Which among the following is true for the determinant of a matrix?

Options: 

 

A. The determinant of a diagonal matrix is the product of its diagonal entries.

B. If one row of a matrix is a scalar multiple of another, the determinant is 1.

C. If one row of a matrix is a scalar multiple of another, the determinant is 0.

D. The determinant of a permutation matrix can only be 1.

Answer: [ A ] [ C ] 

Q11.  Which among the Eigen Values of matrix A ? 

Options: 

A. 1, 3, -3

B. 1, 3, 3

C. -1, 3, 3

D. 1, -3, -3

Answer: [ D ] 

Q12. Find Nullity of A ? 

Answer: 2

Q13. Let A = Suppose the eigen values corresponding to AAT are a,b and c, then find the value of ab+bc+ca. 

Options: 

A. 9 

B. 0 

C. 81

D. 18

Answer: [ B ] 0 

Conclusion: 

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The proofs are given to the above answers from the previous assignments. The detailed solutions will be provided soon. 

Also Read: NPTEL Data Science for Engineers Week 1 Answers 2025