# NPTEL Data Science for Engineers Assignment 2 Answers 2023

NPTEL Data Science for Engineers Assignment 2 Answers 2023:- All the Answers provided below to help the students as a reference, You must submit your assignment at your own knowledge.

## NPTEL Data Science For Engineers Week 2 Assignment Answers 2023

1. Are the vectors [−2 4], [7 −2] and [3 −6] linearly independent?

• Yes
• No

2. Does the set, S={(1,1),(1,2)} spans R2?

• Yes
• No

3. Consider the following system of linear equations of the form Ax=b:1
2x−3y+6z=14
x+y−2z=−3
Which among the following are correct?

• [ 1−4 0 ] is a solution to Ax=b
• [ 0 2 1 ] is a solution to Ax=b
• [ 1 −4 0 ] is a solution to Ax=0
• [ 0 2 1 ] is a solution to Ax=0

Consider the following systerm of linear equation:
x+y+z=−2
x+2y−z=1
2x+ay+bz=2

4. Find the conditions on a and b for which the above system has no solution.

• 2a+b−6=0
• a≠4, 2a+b−6= 0
• a=4, b = −2
• 2a+b−6 ≠ 0

5. Find the conditions on a and b for which the above system has a unique solution.

• 2a+b−6=0
• a≠4, 2a+b−6= 0
• a=4, b = −2
• 2a+b−6 ≠ 0

6. Find the conditions on a and b for which the above system has infite number of solutions.

• 2a+b−6=0
• a≠4, 2a+b−6= 0
• a=4, b = −2
• 2a+b−6 ≠ 0

7. Identify the number of free variable from the above rwo echelon matrix.

• 0
• 1
• 2
• 3

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

• It has infinite number of solutions.
• It has a unique solution.
• It has no solution.

9. For what values of a are matrix

not invertible?

• a=1
• a=−2
• a=−1
• a=2

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

• The determinant of a diagonal matrix is the product of its diagonal entries.
• If one row of a matrix is a scalar multiple of another, the determinant is 1.
• If one row of a matrix is a scalar multiple of another, the determinant is 0.
• The determinant of a permutation matrix can only be 1.

11. Which among the following are the eigenvalues of matrix

• 1, 3, −3
• 1, 3, 3
• −1, 3, 3
• 1, −3, −3

13. Let A= [−1 2 2]. Suppose the eighen values corresponding to AAT are a,b and c, then find the value of ab+bc+ca.

• 9
• 0
• 81
• 18

## NPTEL Data Science for Engineers Assignment 2 Answers 2022 [July 2022]

1. The trace of a 3 x 3 matrix A is 9. A has an eigenvalue 9 of multiplicity 2. Find the determinant of A.

a. 27
b. -729
c. -162
d. 9

2. Which of the following vector sets is/are orthogonal?

a) V1=[5−2 3]T,V2=[−2 4 6]T
b) V1=[1 0 −2]T,V2=[1 4 5]T
c) V1=[1 −2 4]T,V2=[2 5 2]T
d) V1=[1 −2 4]T,V2=[−1 4]T

• a)
• a) and c)
• b) and c)
• a), b), and c)

3. If A=[7645],then the value of |A5−A4| is

a. 0
b. 6
c. 1
d. 5

4. The inverse of the matrix M=[1233695108]  is

5. Which of the following is true about orthonormal vectors?

a. All orthonormal vectors are not orthogonal
b. All orthonormal vectors are orthogonal
c. Two vectors are orthonormal to each other if their dot product is 0
d. Orthonormal vectors are orthogonal vectors with unit magnitude

6. Which of the following sets of column vectors form a basis for R4?

7. Let λ1=1 and λ2=2 be the eigenvalues, and v1=[2−2]T and v2=[31]T be the eigenvectors of a real matrix A. Let B be a projection matrix given as B=[v1v2]. Compute B−1AB.

8. How many solutions does the system of linear equations  15x+20y=25,21x+28y=35 have?

a. Infinite solutions
b. No solution
c. Exactly one solution
d. Cannot be determined

9. Given the matrix [−31121214], the eigenvectors are

10. Consider the matrix A=[−9383878−56658−3−5−9]. The columns of matrix A form a basis for the null space of another square matrix B. Find the rank of the matrix B.

a. 3
b. 1
c. 2
d. 4

## What is Data Science for Engineers?

Data Science for Engineers is a fun-filled course where Domain Certification helps learners to gain expertise in a specific Area/Domain. This can be helpful for learners who wish to work in a particular area as part of their job or research or for those appearing for some competitive exam or becoming job-ready or specialising in an area of study.  Every domain will comprise Core courses and Elective courses. Once a learner completes the requisite courses per the mentioned criteria, you will receive a Domain Certificate showcasing your scores and the domain of expertise.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of the average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF THE AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

NPTEL Registration Steps [July – Dec 2022]
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## NPTEL Data Science for Engineers Assignment 2 Answers [Jan 2022]

Q1. If A is [7645][, then the value of |A5−A4| is _________

(A) 6
(B) 5
(C) 0
(D)1

Q2. Which of the following sets of column vectors form a basis for R4?

(A)

(B)

(C)

(D)  None of the options

Q3. Determinant of the matrix M=

is ______________

(A)348
(B) 353
(C) 340
(D) 345

Q4. Rank of the matrix M=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢−18−36−63−363−9−63−4−8−14−8−6−2−1410203520−5535−12−24−42−24−8−6−4248148−1214⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥ is __________

(A) 2
(B) 5
(C) 3
(D) 1

Q5. Given the matrix A=⎡⎣⎢633189955⎤⎦⎥, B=⎡⎣⎢186453⎤⎦⎥, C=[001005]. If D=CAB exists, then the value at D21 is

(A) 517
(B) 525
(C) 528
(D) 531

Q6. The system of linear equations y+31z+2ax=0,y+31z+32x=0 and 5y+155z+160x=0 has a non-trivial solution if a is __________

(A) 17
(B) 16
(C) –
(D) 2 None of the options

Q7. Given the matrix A=⎡⎣⎢⎢⎢1−3−22−3650−25−1−720−78⎤⎦⎥⎥⎥, the smallest eigen value of the matrix A is ___________

(A) -6.41
(B) -0.48
(C) 3.63
(D) -8.31

Q8. If A=⎡⎣⎢−8−8−6−8−7−9−6−7−4⎤⎦⎥ and B=⎡⎣⎢−6−42−4−3−21−9−8−56−7⎤⎦⎥, the rank of the matrix AB is ______________

(A) 1
(B) 2
(C) 3
(D) None of the given options

Q9. The trace of the 3×3 matrix A is 16. A has an eigenvalue 7 of multiplicity 2. Find the determinant of A.

(A) 93
(B) 99
(C) 98
(D) 91