Data Science for Engineers Assignment 2 Nptel Answers

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NPTEL Data Science for Engineers Assignment 2 Answers ( Jan-Apr 2025)

A) Yes
B) No

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Does the set, S={(1,1),(1,2)}S = \{ (1, 1), (1, 2) \}, span R2\mathbb{R}^2?
A) Yes
B) No

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Find the conditions on aa and bb for which the system has no solution.

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Find the conditions on aa and bb for which the system has a unique solution.

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Find the conditions on aa and bb for which the system has infinite solutions.

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Identify the number of free variables from the following row echelon matrix.
A) 0
B) 1
C) 2
D) 3

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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.

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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 (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

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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

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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

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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.

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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

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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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NPTEL Data Science for Engineers Assignment 2 Answers JULY-DEC 2023

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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 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=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

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