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May 2026 term · Mathematics for Data Science II · BSMA1003

Mathematics for Data Science II Quiz 1: 19 July 2026 (May 2026 term)

The IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 1 paper sat on 19 Jul 2026, in the May 2026 term: 14 questions for 52 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
14
Marks
52
Duration
120 min
MCQ
2
MSQ
4
Written
8
Take as mock testPractise with answers

Updated

Official paper: Maths2 16 Jul 26 · No negative marking.

Question 1

+4 marksOne correct option

Let be a matrix such that . Suppose is a matrix obtained from by swapping the second and third rows, and then multiplying the first row by . Which of the following options is correct?

  1. A

    .

  2. B

    —

  3. C

    —

  4. D

    —

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Correct answer

  • B

    —

Question 1 on its own page

Question 2

+4 marksOne or more correct options

Let . Choose the correct options.

Select all that apply.

  1. A

    and rank .

  2. B

    and rank .

  3. C

    The matrix is in the reduced row echelon form (RREF).

  4. D

    The reduced row echelon form (RREF) of is .

  5. E

    rank rank .

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Correct answers

  • B

    and rank .

  • C

    The matrix is in the reduced row echelon form (RREF).

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Question 3

+4 marksOne or more correct options

Consider the vector space

The subset

is a linearly independent subset of . Which of the following matrices are vectors in such that is a basis for ?

Consider the vector space
Consider the vector space

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
  5. E
    Figure from the original question paper
Show answer

Correct answers

  • B
    Figure from the original question paper
  • C
    Figure from the original question paper
Question 3 on its own page

Question 4

+4 marksWritten answer

If is a linear combination of the vectors as , then find the value of .

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Question 5

+4 marksWritten answer

Let be an invertible -matrix such that . Find ?

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Question 6

+4 marksWritten answer

Let

If forms a subspace of , then find the dimension of . Otherwise, enter the number as the answer.

Let
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Question 7

+4 marksWritten answer

Define a -matrix as . Find the rank of the matrix .

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Question 8

+4 marksWritten answer

Consider the vectors and in , for some . Find the number of values of for which the given three vectors are linearly dependent in .

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Question 9

+5 marksOne or more correct options

denotes the vector space consisting of real square matrices of order 3 with usual matrix addition and scalar multiplication. Consider the following matrices:

Use the given information to answer the subquestions.

denotes the vector space consisting of real square matrices of order 3 with usual matrix addition and scalar multiplicat

Which of the following options are correct?

Select all that apply.

  1. A

    , where denotes the zero matrix of order 3.

  2. B

    , where denotes the zero matrix of order 3.

  3. C

    , where denotes the zero matrix of order 3.

  4. D

    The pair is unique for which holds, where denotes the zero matrix of order 3.

  5. E

    There is more than one pair such that .

Show answer

Correct answers

  • B

    , where denotes the zero matrix of order 3.

  • D

    The pair is unique for which holds, where denotes the zero matrix of order 3.

Question 9 on its own page

Question 10

+4 marksOne correct option

denotes the vector space consisting of real square matrices of order 3 with usual matrix addition and scalar multiplication. Consider the following matrices:

Use the given information to answer the subquestions.

denotes the vector space consisting of real square matrices of order 3 with usual matrix addition and scalar multiplicat

Which of the following options is true?

  1. A

    is a linearly independent set.

  2. B

    is a linearly independent set.

  3. C

    is a linearly dependent set.

  4. D

    is a linearly dependent set.

Show answer

Correct answer

  • A

    is a linearly independent set.

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Question 11

+5 marksOne or more correct options

Let be a coefficient matrix, and be a column matrix to a system of linear equations with variables, , given by where . Use this information to answer the given subquestions.

Let denotes the column space of . Choose the correct options.

Select all that apply.

  1. A

    If , then there exists vector satisfying .

  2. B

    If , then there exists a unique vector satisfying .

  3. C

    If there exists a vector satisfying the , then .

  4. D

    If , then the system of linear equations is consistent.

  5. E

    If , then the system of linear equations is inconsistent.

Show answer

Correct answers

  • A

    If , then there exists vector satisfying .

  • C

    If there exists a vector satisfying the , then .

  • D

    If , then the system of linear equations is consistent.

Question 11 on its own page

Question 12

+4 marksWritten answer

Let be a coefficient matrix, and be a column matrix to a system of linear equations with variables, , given by where . Use this information to answer the given subquestions.

Let

and

. Find the value of , up to two decimal places, such that the system of linear equations does not have any solution.

Let
Let
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Question 13

+1 markWritten answer

denotes the vector space consisting of real square matrices of order 3 with usual matrix addition and scalar multiplication. Consider the following matrices:

Use the given information to answer the subquestions.

denotes the vector space consisting of real square matrices of order 3 with usual matrix addition and scalar multiplicat
Show answer

A written answer, not marked automatically.

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Question 14

+1 markWritten answer

Let be a coefficient matrix, and be a column matrix to a system of linear equations with variables, , given by where . Use this information to answer the given subquestions.

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