Quiz Space

Mathematics for Data Science II · Quiz 1 · 15 Mar 2026 · January 2026 term

Question 8: Which of the following subsets are subspaces of under the…

Question 8

+4 marksOne or more correct options

Which of the following subsets are subspaces of under the usual addition and scalar multiplication?

Select all that apply.

  1. A

    .

  2. B

    .

  3. C

    .

  4. D

    .

Show answer

Correct answers

  • B

    .

  • C

    .

Video solution

The video solution to this question is being recorded and will play here. Until then, the answer key is above.

See the whole paperTake it as a mock test

Question 8 of 45 in the IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 1 paper sat on 15 Mar 2026, in the January 2026 term (Maths2 15 Mar 26). It carries 4 marks.

More questions from this paper

  1. Q1Figure question
  2. Q2Figure question
  3. Q3Figure question
  4. Q4Consider a subspace of . Which of the following options describes a basis of ?
  5. Q5Consider a subspace of . Which of the following options describes a basis of ?
  6. Q6Consider a subspace of . Which of the following options describes a basis of ?
  7. Q7Which of the following subsets are subspaces of under the usual addition and scalar multiplication?
  8. Q9Which of the following subsets are subspaces of under the usual addition and scalar multiplication?
  9. Q10where are distinct real numbers. Which of the following statements are correct?
  10. Q11where are distinct real numbers. Which of the following statements are correct?
  11. Q12where are distinct real numbers. Which of the following statements are correct?
  12. Q13If is a matrix and is a matrix, then choose the set of correct options.
  13. Q14If is a matrix and is a matrix, then choose the set of correct options.
  14. Q15If is a matrix and is a matrix, then choose the set of correct options.
  15. Q16A company produces two types of gadgets, A and B. • Each gadget A requires 2 hours of assembly and 3 hours of testing. …
  16. Q17A company produces two types of gadgets, A and B. • Each gadget A requires 2 hours of assembly and 3 hours of testing. …
  17. Q18A company produces two types of gadgets, A and B. • Each gadget A requires 2 hours of assembly and 3 hours of testing. …
  18. Q19Suppose and . Let be a vector defined as such that and . Find the value of .
  19. Q20Suppose and . Let be a vector defined as such that and . Find the value of .
  20. Q21Suppose and . Let be a vector defined as such that and . Find the value of .
  21. Q22Suppose the vectors , and in are linearly dependent. Find the value of .
  22. Q23Suppose the vectors , and in are linearly dependent. Find the value of .
  23. Q24Suppose the vectors , and in are linearly dependent. Find the value of .
  24. Q25Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: • On …
  25. Q26Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: • On …
  26. Q27Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: • On …
  27. Q28Suppose the rank of the matrix is . Based on the above data, answer the given subquestions. Find .
  28. Q29Suppose the rank of the matrix is . Based on the above data, answer the given subquestions. Find .
  29. Q30Suppose the rank of the matrix is . Based on the above data, answer the given subquestions. Find .
  30. Q31Suppose the rank of the matrix is . Based on the above data, answer the given subquestions. Find .
  31. Q32Suppose the rank of the matrix is . Based on the above data, answer the given subquestions. Find .
  32. Q33Suppose the rank of the matrix is . Based on the above data, answer the given subquestions. Find .
  33. Q34Which of the following options is correct?
  34. Q35Which of the following options is correct?
  35. Q36Which of the following options is correct?
  36. Q37Consider the vector space with the addition and scalar multiplication operations from the correct option of the previou…
  37. Q38Consider the vector space with the addition and scalar multiplication operations from the correct option of the previou…
  38. Q39Consider the vector space with the addition and scalar multiplication operations from the correct option of the previou…
  39. Q40Suppose the rank of the matrix is . Based on the above data, answer the given subquestions.
  40. Q41Consider a subset of . Based on the above data, answer the given subquestions.
  41. Q42Suppose the rank of the matrix is . Based on the above data, answer the given subquestions.
  42. Q43Consider a subset of . Based on the above data, answer the given subquestions.
  43. Q44Suppose the rank of the matrix is . Based on the above data, answer the given subquestions.
  44. Q45Consider a subset of . Based on the above data, answer the given subquestions.