Data Science for Engineers Assignment 2 Nptel Answers
Are you looking for NPTEL Data Science for Engineers Assignment 2 Answers ? You’ve come to the right place! Access the most accurate answers at Progiez
Table of Contents
Nptel Data Science for Engineers Assignment 2 Answers (July-Dec 2025)
Question 1. Are the vectors [−2 4]T[-2\ 4]^T and [3 −6]T[3\ -6]^T linearly independent?
a) Yes
b) No
Question 2. Does the set, S={(1,1),(1,2)}S = \{(1,1), (1,2)\} span R2\mathbb{R}^2?
a) Yes
b) No
Question 3. Consider the following system of linear equations of the form Ax=bAx = b: 2x−3y+6z=14x+y−2z=−32x – 3y + 6z = 14 \\ x + y – 2z = -3
Which among the following are correct?
a) [1−40]\begin{bmatrix} 1 \\ -4 \\ 0 \end{bmatrix} is a solution to Ax=bAx = b
b) [021]\begin{bmatrix} 0 \\ 2 \\ 1 \end{bmatrix} is a solution to Ax=bAx = b
c) [1−40]\begin{bmatrix} 1 \\ -4 \\ 0 \end{bmatrix} is a solution to Ax=0Ax = 0
d) [021]\begin{bmatrix} 0 \\ 2 \\ 1 \end{bmatrix} is a solution to Ax=0Ax = 0
Question 4. Find the conditions on aa and bb for which the system has no solution: x+y+z=−2x+2y−z=12x+ay+bz=2x + y + z = -2 \\ x + 2y – z = 1 \\ 2x + ay + bz = 2
a) 2a+b−6=02a + b – 6 = 0
b) a≠4, 2a+b−6=0a \ne 4,\ 2a + b – 6 = 0
c) a=4, b=−2a = 4,\ b = -2
d) 2a+b−6≠02a + b – 6 \ne 0
Question 5. Find the conditions on aa and bb for which the above system has a unique solution.
a) 2a+b−6=02a + b – 6 = 0
b) a≠4, 2a+b−6=0a \ne 4,\ 2a + b – 6 = 0
c) a=4, b=−2a = 4,\ b = -2
d) 2a+b−6≠02a + b – 6 \ne 0
Question 6. Find the conditions on aa and bb for which the system has infinite number of solutions.
a) 2a+b−6=02a + b – 6 = 0
b) a≠4, 2a+b−6=0a \ne 4,\ 2a + b – 6 = 0
c) a=4, b=−2a = 4,\ b = -2
d) 2a+b−6≠02a + b – 6 \ne 0
Question 7. Identify the number of free variables from the row echelon matrix: [100001010032102313]\begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 3 & 2 \\ 1 & 0 & 2 & 3 & 1 & 3 \\ \end{bmatrix}
a) 0
b) 1
c) 2
d) 3
Question 8. Which among the following is correct for the above system Ax=bAx = b?
a) It has infinite number of solutions.
b) It has a unique solution.
c) It has no solution.
Question 9. For what values of aa is matrix A=[a−21a+3]A = \begin{bmatrix} a & -2 \\ 1 & a + 3 \end{bmatrix} not invertible?
a) a = 1
b) a = −2
c) a = −1
d) a = 2
Question 10. Which among the following is true for the determinant of a matrix?
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.
Question 11. Which among the following are the eigenvalues of matrix A=[54−481−4168]A = \begin{bmatrix} 5 & 4 & -4 \\ 8 & 1 & -4 \\ 1 & 6 & 8 \end{bmatrix}?
a) 1, 3, −3
b) 1, 3, 3
c) −1, 3, 3
d) 1, −3, −3
Question 12. Find the nullity of A=[110−3−30−21141−1−1−1]A = \begin{bmatrix} 1 & 1 & 0 & -3 & -3 \\ 0 & -2 & 1 & 1 & 4 \\ 1 & -1 & -1 & -1 \end{bmatrix}
a) 1
b) 2
c) 3
d) 4
Question 13. Let A=[−122]A = \begin{bmatrix} -1 \\ 2 \\ 2 \end{bmatrix}. Suppose the eigenvalues corresponding to AATAA^T are a,b,a, b, and cc, then find the value of ab+bc+caab + bc + ca.
a) 9
b) 0
c) 81
d) 18
NPTEL Data Science for Engineers Assignment 2 Answers ( Jan-Apr 2025)
A) Yes
B) No
- Does the set, S={(1,1),(1,2)}S = \{ (1, 1), (1, 2) \}, span R2\mathbb{R}^2?
A) Yes
B) No
- Find the conditions on aa and bb for which the system has no solution.
- Find the conditions on aa and bb for which the system has a unique solution.
- Find the conditions on aa and bb for which the system has infinite solutions.
- Identify the number of free variables from the following row echelon matrix.
A) 0
B) 1
C) 2
D) 3
- Which among the following is correct for the system Ac=bAc = b?
A) It has infinite number of solutions.
B) It has a unique solution.
C) It has no solution.
- Which among the following is true for the determinant of a matrix?
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.
NPTEL Data Science for Engineers Assignment 2 Answers (July-Dec 2024 )
Session: JUL-DEC 2024
Q1. Are the vectors [−2 4],[7−2]
and [3−6] linearly independent?
Yes
No
Answer: No
Q2.Does the set, S={(1,1),(1,2)} spans R2?
Yes
No
Answer: Yes
For answers or latest updates join our telegram channel: Click here to join
These are Nptel Data Science for Engineers Week 2 Assignment Answers
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?
a) [1−4 0] is a solution to Ax=b
b) [0 2 1] is a solution to Ax=b
c) [1 −4 0 ] is a solution to Ax=0
d) [ 0 2 1 ] is a solution to Ax=0
Answer: a),d)
Q4.Consider the following systerm of linear equation:
x+y+z=−2
x+2y−z=1
2x+ay+bz=2
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
For answers or latest updates join our telegram channel: Click here to join
These are Nptel Data Science for Engineers Week 2 Assignment 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
For answers or latest updates join our telegram channel: Click here to join
See also Data Science for Engineers Nptel Assignment 5 Answers
These are Nptel Data Science for Engineers Week 2 Assignment Answers
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.
For answers or latest updates join our telegram channel: Click here to join
These are Nptel Data Science for Engineers Week 2 Assignment Answers
Q9. For what values of a are matrix A = [a−21a+3] not invertible?
a = 1
a = −2
a = −1
a = 2
Answer: a = −2
a = −1
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: 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 0.
Q11.Which among the following are the eigenvalues of matrix A
1, 3, −3
1, 3, 3
−1, 3, 3
1, −3, −3
Answer: 1, −3, −3
Q12.Find the nullity of A
Answer: 2
Q13.Let A=[−1 2 2] .Suppose the eigen values corresponding to AAT are a,b and c, then find the value of ab+bc+ca.
9
0
81
18
Answer:0
For answers or latest updates join our telegram channel: Click here to join
These are Nptel Data Science for Engineers Week 2 Assignment Answers
All Weeks of Data Science for Engineers: Click here
For answers to additional Nptel courses, please refer to this link: Check here
NPTEL Data Science for Engineers Assignment 2 Answers (JAN-APR 2024 )
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
For answers or latest updates join our telegram channel: Click here to join
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=−3
Which 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=−2
x+2y−z=1
2x+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
For answers or latest updates join our telegram channel: Click here to join
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
For answers or latest updates join our telegram channel: Click here to join
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.
For answers or latest updates join our telegram channel: Click here to join
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
For answers or latest updates join our telegram channel: Click here to join
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
More Solutions of Data Science for Engineers: Click Here
More Nptel Courses: Click here
NPTEL Data Science for Engineers Assignment 2 Answers JULY-DEC 2023
Course Name: Data Science for Engineers
Course Link: Click Here
Q1. Does the set, S={(1,1),(1,2)} spans R2?
a. Yes
b. No
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 AAT 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=1
2×1+5×2+7×3=2
2×1+4×2+6×3=2
Choose 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
More Solutions of Data Science for Engineers: Click Here
More Nptel Courses: Click here
