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MLF · Eigenvalues & diagonalization

9 questions · 21 marks · 3 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Machine Learning Foundations

Eigenvalues & diagonalization

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Q1NAT3 Marks·Write the number
Key ↓
Your answer:
Q2NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q3–Q4
Based on the above data, answer the given subquestions.
Q3MSQ2 Marks·Choose all correct options
Key ↓
Which of the following is/are true?
1. AA is an orthogonal matrix
2. BA is invertible
3. CA is symmetric
Q4MCQ3 Marks·Choose one option
Key ↓
Which of the following is true?
1. AA does not have real eigenvalues
2. BA has two distinct real eigenvalues
3. CA has two real eigenvalues, not necessarily distinct
Read the passage below, then answer Q5–Q7
There is no common data for this question. There are three independent sub-questions for which you have to answer True/False.
Q5MCQ2 Marks·Choose one option
Key ↓
If a square matrix A is diagonalizable, then A is invertible.
1. ATrue
2. BFalse
Q6MCQ1 Mark·Choose one option
Key ↓
The eigenvalues of a real symmetric matrix are real.
1. ATrue
2. BFalse
Q7MCQ2 Marks·Choose one option
Key ↓
A square matrix A of shape n x n is diagonalizable if and only if it has n distinct eigenvalues.
1. ATrue
2. BFalse

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q8
Based on the above data, answer the given subquestions
Q8NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Read the passage below, then answer Q9
Based on the above data, answer the given subquestions.
Q9NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q11024

Q20

Q3A, B

Q4A

Q5B

Q6A

Q7B

Q8-11

Q9-125

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.