Quiz Space

Mathematics for Data Science II · End Term · 10 May 2026 · January 2026 term

Question 5: Let be a linear transformation. Let and Suppose that the …

Question 5

+6 marksOne correct option

Let be a linear transformation. Let and Suppose that the matrix representation of with respect to ordered bases for the domain and for the co-domain is given by

. Then which of the following defines the transformation ?

Let be a linear transformation. Let and Suppose that the matrix representation of with respect to ordered bases for
  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • B

    —

See the whole paperTake it as a mock test

Question 5 of 46 in the IIT Madras BS Mathematics for Data Science II (Maths 2) End Term paper sat on 10 May 2026, in the January 2026 term (Maths2 06 May 26). It carries 6 marks.

More questions from this paper

  1. Q1Consider the function defined as follows. Choose the correct option.
  2. Q2Let be a linear transformation given by , and . Choose the correct option from the following:
  3. Q3Let be a square matrix of order . If , which of the following sequences of row operations can be performed on so that t…
  4. Q4Consider the function defined as follows. Choose the correct option.
  5. Q6Let be a linear transformation defined by . Let and Choose the correct option for the matrix representation of with res…
  6. Q7Define a function
  7. Q8Define a function Choose the correct options.
  8. Q9Choose all the subspaces isomorphic to .
  9. Q10Choose all the subspaces isomorphic to .
  10. Q11If is an orthogonal matrix of order 5, then find the nullity of the matrix .
  11. Q12Let be a vector such that . If is the vector obtained from after the anti- clockwise rotation in the -plane by an angle…
  12. Q13Let and be two vectors in . If and are orthogonal to each other, find the value of .
  13. Q14Let and be two vectors in such that and are perpendicular to each other. Find the value of .
  14. Q15Consider the function defined as If the unit direction of the steepest ascent of at is , then find the value of ?
  15. Q16Consider a function defined as . If the unit direction of the steepest descent of at is , then find the value of ?
  16. Q17Let be a linear transformation given by , and . If , find .
  17. Q18is a square matrix of order 4. When the following sequence of row operations are performed on , the result is the ident…
  18. Q19Which of the following points lie in ?
  19. Q20Which of the following points are in ?
  20. Q21What is the dimension of the subspace corresponding to the affine subspace ?
  21. Q22What is the dimension of the subspace corresponding to the affine subspace ?
  22. Q23Consider the function defined as Based on the above data, answer the given subquestions. Consider the following stateme…
  23. Q24Which of the following options depict the correct geometric shape of the boundary of ?
  24. Q25Consider the function defined as Based on the above data, answer the given subquestions. Suppose function describes the…
  25. Q26Suppose denotes the absolute maximum value. Find .
  26. Q27Which of the following options depicts the correct geometric shape of the boundary of ?
  27. Q28Suppose denote the absolute minimum value. Find .
  28. Q29What is the number of critical points inside the domain of ? Write zero if there is no critical point.
  29. Q30Consider the following statements about the function . S1: The range of contains . S2: The domain of the gradient is . …
  30. Q31Find the absolute maximum of over the domain .
  31. Q32Suppose the function describes the pressure in a room at point . If the rate of change of pressure at in the direction …
  32. Q33Find the rank of .
  33. Q34Find the determinant of .
  34. Q35Find the determinant of .
  35. Q36Find the rank of .
  36. Q37Choose all the correct options from the following:
  37. Q38Choose all the correct options from the following:
  38. Q39Let be the real valued function defined by for all . Let denote the tangent plane to the graph of at the point . Based …
  39. Q40Consider the function defined as Based on the above data, answer the given subquestions.
  40. Q41Consider the following domain Suppose is a function defined by Based on the above data, answer the given subquestions.
  41. Q42Let and . Based on the above data, answer the given subquestions.
  42. Q43Let be the real valued function defined by for all . Let denote the tangent plane to the graph of at the point . Based …
  43. Q44Allowed : No Group Comprehension Questions : No Question Pattern Type : NonMatrix Consider the following domain Suppose…
  44. Q45Consider the function defined as Based on the above data, answer the given subquestions.
  45. Q46Let and . Based on the above data, answer the given subquestions.