Nptel Data Science for Engineers Week 2 Assignment Answers 2026
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Nptel Data Science for Engineers Week 2 Assignment Answers 2026
Que.1
Are the vectors
[−2
4],
[7
−2],
and
[3
−6]
linearly independent?
a) Yes
b) No
Que.2
Does the set S = {(1,1), (1,2)} span ℝ²?
a) Yes
b) No
Que.3
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
Que.4
Consider the following system of linear equations:
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.
a) 2a + b − 6 = 0
b) a ≠ 4, 2a + b − 6 = 0
c) a = 4, b = −2
d) 2a + b − 6 ≠ 0
Que.5
Find the conditions on a and b for which the above system has a unique solution.
a) 2a + b − 6 = 0
b) a ≠ 4, 2a + b − 6 = 0
c) a = 4, b = −2
d) 2a + b − 6 ≠ 0
Que.6
Find the conditions on a and b for which the above system has infinite number of solutions.
a) 2a + b − 6 = 0
b) a ≠ 4, 2a + b − 6 = 0
c) a = 4, b = −2
d) 2a + b − 6 ≠ 0
Que.7
In solving the system Ax = b with variables x₁, x₂, x₃, and x₄, Gaussian elimination on the augmented matrix [A | b] led to a row echelon form.
Identify the number of free variables from the above row echelon matrix.
a) 0
b) 1
c) 2
d) 3
Que.8
Which among the following is correct for the above system Ax = b?
a) It has infinite number of solutions
b) It has a unique solution
c) It has no solution
Que.9
For what values of a are matrix
A = [ a −2
1 a+3 ]
not invertible?
a) a = 1
b) a = −2
c) a = −1
d) a = 2
Que.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
Que.11
Which among the following are the eigenvalues of the matrix
A = ⎛
5 4 −4
8 1 −4
16 8 −11
⎞ ?
a) 1, 3, −3
b) 1, 3, 3
c) −1, 3, 3
d) 1, −3, −3
Que.12
Find the nullity of the matrix
A = ⎡
1 1 0 −3
−3 0 −2 1
1 4 1 −1
⎤
Que.13
Let
A = ⎡ −1 2
2 2 ⎤.
Suppose the eigenvalues corresponding to A Aᵀ are a, b, and c. Find the value of ab + bc + ca.
a) 9
b) 0
c) 81
d) 18
Session: JUL-DEC 2024
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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
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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
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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
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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.
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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
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These are Nptel Data Science for Engineers Week 2 Assignment Answers
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