# Data Science for Engineers | Week 2

### Session: JULY-DEC 2023

Course Name: Data Science for Engineers

#### These are NPTEL Data Science for Engineers Assignment 2 Answers

Q1. Are the vectors [−24][−24],[7−2][7−2] and [3−6][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 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

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

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

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 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

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 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

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.

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

Q12. Find the nullity of A=⎡⎣⎢110−3−30−21141−1⎤⎦⎥

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

Course Name: Data Science for Engineers

#### Q1. Does the set, S={(1,1),(1,2)} spans R2?a. Yesb. No

Q2. Find the rank of the matrix M= [124 235 369]
a. 0
b. 1
c. 2
d. 3

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

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. 
b. 
c. 
d. [−11]

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

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

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], 
b. [1−24], [−142]
c. [1−24], [−252]
d. [5−23], [−246]

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