# 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

**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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