Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Mathematics for Data Science II
Affine subspaces
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- MCQ: Exactly 1 option is correct. Negative marking applies.
- MSQ: One or more options correct. Select all to score.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
End Term · 31 Aug 2025 (FN)End Term
Read the passage below, then answer Q1–Q2
Based on the above data, answer the given subquestions.
Q1NAT2 Marks·Write the numberFind the value of k.
Your answer:- Q2NAT1 Mark·Write the number
Find the dimension of the affine subspace S.
Your answer: Read the passage below, then answer Q3–Q4
Based on the above data, answer the given subquestions.
Q3MSQ2 Marks·Choose all correct optionsWhich of the following points lie on T(1,−1)?
- A(0, 0, 1)
- B(0, 1, 0)
- C(1, 0, 0)
- D(2, 0, 1)
- E(1, 1, 1)
- Q4MCQ2 Marks·Choose one option
Let W denote the subspace corresponding to the affine subspace T(1,−1). Which of the following is a basis for the orthogonal complement of W?
- A{(1,−1,−1)}
- B{(−1,−1,−1)}
- C{(1, 1,−1)}
- D{(1,−1, 1)}
End Term · 31 Aug 2025 (AN)End Term
Read the passage below, then answer Q5–Q6
Based on the above data, answer the given subquestions.
Q5NAT2 Marks·Write the numberFind the value of k.
Your answer:- Q6NAT1 Mark·Write the number
Your answer: Read the passage below, then answer Q7–Q8
Based on the above data, answer the given subquestions.
Q7MSQ2 Marks·Choose all correct optionsWhich of the following are possible candidates for v ?
- A(2, 1, 2)
- B(0, 7, 0)
- C(1,−2, 0)
- D(2, 0,−1)
- Q8MCQ2 Marks·Choose one option
Which of the following is a basis for U ?
- A{(1,−1,−1), (1, 3, 2)}
- B{(1, 2, 3), (−1,−1,−1)}
- C{(0, 1,−1), (0,−1, 1)}
- D{(1, 2, 3), (0,−1, 1)}