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

Question 3: Let denote the standard inner product on , i.e., for and …

Question 3

+4 marksOne or more correct options

Let denote the standard inner product on , i.e., for and in . For a vector , consider a linear transformation defined as where . Which of the following options is (are) true for ?

Select all that apply.

  1. A

    is one-one for all .

  2. B

    is onto for all .

  3. C

    is not one-one for every .

  4. D

    There exists a such that is an isomorphism.

Show answer

Correct answers

  • B

    is onto for all .

  • C

    is not one-one for every .

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Question 3 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.

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