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January 2026 term · Mathematics for Data Science II · BSMA1003

Mathematics for Data Science II Quiz 2: 12 April 2026 (January 2026 term)

The IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 2 paper sat on 12 Apr 2026, in the January 2026 term: 17 questions for 53 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
17
Marks
53
Duration
120 min
MCQ
2
MSQ
6
Written
9
Take as mock testPractise with answers

Updated

Official paper: Maths2 06 Apr 26 · No negative marking.

Question 1

+4 marksOne correct option

Consider the system of linear equations given by Suppose represents the affine space of solutions of , and let be the subspace in corresponding to the affine space . Choose the correct option from the following.

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • B

    —

Question 1 on its own page

Question 2

+4 marksOne correct option

Let be a linear transformation such that Which of the following statements is correct?

  1. A

    is the identity transformation.

  2. B

    maps every vector in to a vector with at least one zero component.

  3. C

    is not injective.

  4. D

    .

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Correct answer

  • C

    is not injective.

Question 2 on its own page

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.

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Correct answers

  • B

    is onto for all .

  • C

    is not one-one for every .

Question 3 on its own page

Question 4

+4 marksOne or more correct options

Let and be square matrices of the same order . Which of the following statements are sufficient to conclude that is equivalent to ?

Select all that apply.

  1. A

    .

  2. B

    .

  3. C

    The set of columns of and the set of columns of are both linearly dependent subsets of .

  4. D

    There exists a matrix such that is equivalent to , and is equivalent to .

  5. E

    There exist invertible matrices and of order such that

Show answer

Correct answers

  • B

    .

  • D

    There exists a matrix such that is equivalent to , and is equivalent to .

  • E

    There exist invertible matrices and of order such that

Question 4 on its own page

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

    .

Question 5 on its own page

Question 6

+4 marksOne or more correct options

Let be defined by Which of the following statements are true?

Select all that apply.

  1. A

    is injective if and only if .

  2. B

    when .

  3. C

    The image of is a plane in for all .

  4. D

    The vector is in for some .

  5. E

    There does not exist a non-zero vector such that .

Show answer

Correct answers

  • D

    The vector is in for some .

  • E

    There does not exist a non-zero vector such that .

Question 6 on its own page

Question 7

+4 marksWritten answer

Suppose that is a linear transformation given by . Let be the matrix representation of with respect to the ordered standard bases for both domain and co-domain. If is equivalent to , find the rank of .

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Question 7 on its own page

Question 8

+4 marksWritten answer

Let be a linear transformation defined by Based on the above data, answer the given subquestions.

Let be a vector in the kernel of such that .Find the value of up to two decimal places.

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Question 9

+2 marksWritten answer

Let be a linear transformation defined by Based on the above data, answer the given subquestions.

Consider the set Find the -coordinate of the point of intersection of the image of under , that is, the set , and the -axis in .

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Question 10

+4 marksWritten answer

Let be a linear transformation defined by . Let . Define the linear transformation Based on the above data, answer the given subquestions.

Find the dimension of the image of .

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Question 11

+3 marksOne or more correct options

Let be a linear transformation defined by . Let . Define the linear transformation Based on the above data, answer the given subquestions.

Figure from the original question paper

Select all that apply.

  1. A

    .

  2. B

    .

  3. C

    .

  4. D

    .

Show answer

Correct answers

  • A

    .

  • C

    .

Question 11 on its own page

Question 12

+3 marksWritten answer

Let . Based on the above data, answer the given subquestions.

Find the dimension of .

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Question 13

+3 marksOne or more correct options

Let . Based on the above data, answer the given subquestions.

Which of the following sets form an orthonormal basis for ? Choose all correct options.

Select all that apply.

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answers

  • A

    —

  • B

    —

Question 13 on its own page

Question 14

+3 marksWritten answer

Let . Based on the above data, answer the given subquestions.

Suppose represents the projection transformation onto . If find .

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Question 15

+1 markWritten answer

Let be a linear transformation defined by Based on the above data, answer the given subquestions.

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Question 16

+1 markWritten answer

Let be a linear transformation defined by . Let . Define the linear transformation Based on the above data, answer the given subquestions.

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Question 16 on its own page

Question 17

+1 markWritten answer

Let . Based on the above data, answer the given subquestions.

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Question 17 on its own page