# Nptel Data Science for Engineers Week 2 Assignment Answers

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## Nptel Data Science for Engineers Week 2 Assignment Answers

Session: JUL-DEC 2024

Q1. Are the vectors [−2 4],[7−2]
and [3−6] linearly independent?
Yes
No

Q2.Does the set, S={(1,1),(1,2)} spans R2?
Yes
No

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

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

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

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

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

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 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

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

Q12.Find the nullity of A

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