The IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 2 paper sat on 16 Aug 2026, in the May 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.
Which one of the following statements is true?
Every pair of equivalent matrices is similar.
If two matrices are similar, then they are equivalent.
Two matrices are equivalent if and only if they have the same determinant.
If two matrices represent the same linear transformation with respect to different ordered bases of the domain and different ordered bases of the codomain, then they are similar.
Correct answer
If two matrices are similar, then they are equivalent.
Which one of the following statements is true ?
A set of linearly independent vectors in an -dimensional vector space need not form a basis.
If is onto, then .
If a finite-dimensional vector space has dimension , then every set of more than vectors in is linearly dependent.
The column space of a matrix is always equal to its row space.
Correct answer
If a finite-dimensional vector space has dimension , then every set of more than vectors in is linearly dependent.
Which of the following statements are correct?
If , then
For vectors , .
An affine subspace can be written as , where is a vector subspace of .
Let be an matrix. The solution set of is always a vector subspace of , for every .
Correct answers
If , then
For vectors , .
An affine subspace can be written as , where is a vector subspace of .
Correct answers
is true but is false.
Both and are true.
Both and are true.
is false but is true.
is true.
Correct answers
is true but is false.
is false but is true.
is true.
.
.
is a linear transformation between finite-dimensional vector spaces such that . If is one-to-one, then is onto.
.
is a linear transformation between finite-dimensional vector spaces. If , then cannot be one-to-one.
Correct answers
.
is a linear transformation between finite-dimensional vector spaces such that . If is one-to-one, then is onto.
.
is a linear transformation between finite-dimensional vector spaces. If , then cannot be one-to-one.
A written answer, not marked automatically.
A written answer, not marked automatically.
Based on the above data, answer the given subquestions.
If belongs to the column space of , find .
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Based on the above data, answer the given subquestions.
Consider the linear transformation . Which one of the following is correct?
is one-to-one but not onto.
is onto but not one-to-one.
is both one-to-one and onto.
is neither one-to-one nor onto.
Correct answer
is neither one-to-one nor onto.
Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Let with the standard inner product. Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Let with the standard inner product. Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Let with the standard inner product. Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
