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.
These are NPTEL Data Science for Engineers Assignment 2 Answers
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 AAT 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.
