Quiz Space

Mathematics for Data Science II · Quiz 2 · 12 Apr 2026 · January 2026 term

Question 5: Let be a linear transformation such that . Let . Choose a…

Question 5

+4 marksOne or more correct options

Let be a linear transformation such that . Let . Choose all the correct options.

Select all that apply.

  1. A

    is a two-dimensional subspace of .

  2. B

    The vector lies in .

  3. C

    .

  4. D

    The restriction is not injective.

Show answer

Correct answers

  • A

    is a two-dimensional subspace of .

  • C

    .

See the whole paperTake it as a mock test

Question 5 of 17 in the IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 2 paper sat on 12 Apr 2026, in the January 2026 term (Maths2 06 Apr 26). It carries 4 marks.

More questions from this paper

  1. Q1Consider the system of linear equations given by Suppose represents the affine space of solutions of , and let be the s…
  2. Q2Let be a linear transformation such that Which of the following statements is correct?
  3. Q3Let denote the standard inner product on , i.e., for and in . For a vector , consider a linear transformation defined a…
  4. Q4Let and be square matrices of the same order . Which of the following statements are sufficient to conclude that is equ…
  5. Q6Let be defined by Which of the following statements are true?
  6. Q7Suppose that is a linear transformation given by . Let be the matrix representation of with respect to the ordered stan…
  7. Q8Let be a vector in the kernel of such that .Find the value of up to two decimal places.
  8. Q9Consider the set Find the -coordinate of the point of intersection of the image of under , that is, the set , and the -…
  9. Q10Find the dimension of the image of .
  10. Q11Let be a linear transformation defined by . Let . Define the linear transformation Based on the above data, answer the …
  11. Q12Find the dimension of .
  12. Q13Which of the following sets form an orthonormal basis for ? Choose all correct options.
  13. Q14Suppose represents the projection transformation onto . If find .
  14. Q15Let be a linear transformation defined by Based on the above data, answer the given subquestions.
  15. Q16Let be a linear transformation defined by . Let . Define the linear transformation Based on the above data, answer the …
  16. Q17Let . Based on the above data, answer the given subquestions.