# Data Science for Engineers | Week 2

**Session: JULY-DEC 2023**

**Course Name: Data Science for Engineers**

**Course Link: Click Here**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q1. Are the vectors [−24][−24],[7−2][7−2] and [3−6][3−6] linearly independent?**

Yes

No

**Answer: No**

**Q2. Does the set, S={(1,1),(1,2)} spans R2?**

Yes

No

**Answer: Yes**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q3. Consider the following system of linear equations of the form Ax=b: 2x−3y+6z=14 x+y−2z=−3Which among the following are correct?**

⎡⎣⎢1−40⎤⎦⎥ is a solution to Ax=b

⎡⎣⎢021⎤⎦⎥ is a solution to Ax=b

⎡⎣⎢1−40⎤⎦⎥ is a solution to Ax=0

⎡⎣⎢021⎤⎦⎥ is a solution to Ax=0

Answer: a, d

**Consider the following systerm of linear equation:x+y+z=−2x+2y−z=12x+ay+bz=2**

**Q4. 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

**Answer: a≠4,2a+b−6=0**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q5. 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

**Answer: 2a+b−6≠0**

**Q6. 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

**Answer: a=4,b=−2**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**In solving the system Ax=b in the variables x1,x2,x3 and x4, Gaussian elimination on the Augmented matrix[A|b] led to the following row echelon form**

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

0

1

2

3

**Answer: 1**

**Q8. 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.

**Answer: It has infinite number of solutions.**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q9. For what values of a are matrix A=[a−21a+3] not invertible?**

a=1

a=−2

a=−1

a=2

**Answer: b, c**

**Q10. 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.

**Answer: a, c**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q11. Which among the following are the eigenvalues of matrix**

1, 3, −3

1, 3, 3

−1, 3, 3

1, −3, −3

**Answer: 1, −3, −3**

**Q12. Find the nullity of A=⎡⎣⎢110−3−30−21141−1⎤⎦⎥**

**Answer: 2**

**Q13. Let A=⎡⎣⎢−122⎤⎦⎥. Suppose the eighen values corresponding to AAT are a,b and c, then find the value of ab+bc+ca.**

9

0

81

18

**Answer: 0**

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**Course Name: Data Science for Engineers**

**Course Link: Click Here**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q1. Does the set, S={(1,1),(1,2)} spans R**^{2}?

a. Yes

b. No

^{2}?

**Answer: b. No**

**Q2. Find the rank of the matrix M= [124 235 369]**

a. 0

b. 1

c. 2

d. 3

**Answer: c. 2**

**Q3. Let M be a 2 × 2 matrix, with trace equal to 4 and determinant equal to 3. Find the eighen values of M.**

a. −1, −3

b. −1, 3

c. 1, −3

d. 1, 3

**Answer: d. 1, 3**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q4. Which among the following can be the eigen vector for the matrix A=(12 43)?**

a. [12]

b. [11]

c. [21]

d. [−11]

**Answer: c. [21]**

**Q5. Let A=[−122]. Suppose the eighen values corresponding to AA ^{T} are a,b and c, then find the value of ab+bc+ca.**

a. 9

b. 0

c. 81

d. 18

**Answer: a. 9**

**Q6. Which among the following is true for an n×n matrix A?**

a. If λ is an eighen value of A, then 1/λ is an eighen value of A−1.

b. det(A−1)= (det(A))−1

c. Let B be an n×n matrix. Then det(AB) = det(A)det(B)

d. All of the above

**Answer: c. Let B be an n×n matrix. Then det(AB) = det(A)det(B)**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q7. Check if the following set of vectors are linearly independent.****v1=[2−13], v2=[11−2], v3=[3−38]**

a. Yes

b. No

**Answer: a. Yes**

**Q8. Consider the following system of linear equations:x1+2×2+3×3=12×1+5×2+7×3=22×1+4×2+6×3=2Choose the correct options from the following:**

a. It has infinite number of solutions.

b. It has a unique solution.

c. It has no solution.

**Answer: b. It has a unique solution.**

**Q9. Which of the following set of vectors are orthogonal?**

a. [1−1−2], [201]

b. [1−24], [−142]

c. [1−24], [−252]

d. [5−23], [−246]

**Answer: a. [1−1−2], [201]**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

**Q10. Suppose the eighen values of matrix A are −3,−4,−4,−3, then the determinant of the matrix (A−1) ^{T} is**

a. 0.06

b. -14

c. 0

d. 0.0069

**Answer: d. 0.0069**

**These are NPTEL Data Science for Engineers Assignment 2 Answers**

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