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.
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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
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.