Linear Algebra

MMT-002 important topics

The eGyanKosh units IGNOU has examined most, from 7 past papers. Matched automatically from question wording.

1. Block 2, Unit 6: Matrix Decompositions ↗Asked almost every time: in 6 of 7 papers
2. Block 2, Unit 5: Positive Definiteness ↗Asked almost every time: in 5 of 7 papers
3. Block 1, Unit 2: Jordan Form ↗Asked often: in 4 of 7 papers
4. Block 1, Unit 3: Applications of the Jordan Form ↗Asked sometimes: in 2 of 7 papers
5. Block 1, Unit 1: Similarity ↗Asked sometimes: in 2 of 7 papers
6. Block 2, Unit 4: Unitary Similarity ↗Asked sometimes: in 1 of 7 papers

MMT-002 assignment

The latest MMT-002 assignment is valid for the January 2026 & July 2026 sessions. It carries 100 marks and 30% of your final grade. Due 31 Mar 2026 for the January 2026 session or 30 Sept 2026 for the July 2026 session.

MMT-002 previous-year question papers

Official term-end exam papers for Linear Algebra, published by IGNOU. Each one opens on IGNOU’s website.

• June 2024MMT-002 term-end exam, official PDF↗
• December 2023MMT-002 term-end exam, official PDF↗
• June 2023MMT-002 term-end exam, official PDF↗
• December 2022MMT-002 term-end exam, official PDF↗
• June 2022MMT-002 term-end exam, official PDF↗
• June 2021MMT-002 term-end exam, official PDF↗
• December 2020MMT-002 term-end exam, official PDF↗

Important Linear Algebra questions

The text is taken from IGNOU’s official papers, so open the paper for figures and exact wording.

1. December 2023 · Q4(a) · 2 marks

   Prove that if N is a non-zero nilpotent operator, then N is not diagonlizable.

2. December 2022 · Q3(b) · 3 marks

   Find the QR decomposition of

3. December 2022 · Q4(a) · 3 marks

   Let Ma nd A be a metro city and a nearby small town, respectively. Each year 20% of A’s population moves to M and 5% of M’s population moves to A. What is the long-term effect of this on the populations of M and A? Are they likely to stabilise? Why or why not?

4. December 2022 · Q5 · 2 marks

   Which of the following statements are true? Give reasons for your answers: (i) The sum of two diagonalisable matrices is a diagonalisable matrix. (ii) The only diagonalisable nilpotent matrix is the zero matrix. (iii) There is no unitary matrix having one of its entries 2. (iv) If A is an n × n matrix such that det (A) > 0, then A is a positive definite matrix. (v) If A () n∈ MC has an eigen value with algebraic multiplicity greater than one, then A cannot be normal.

5. June 2021 · Q5(a)

   The sum of two diagonalisable linear operators on a finite-dimensional vector space is diagonalisable.

6. June 2021 · Q5(b)

   Each entry of a positive definite matrix is non-negative.

7. June 2021 · Q5(e)

   Any two distinct eigenvectors of a matrix will be linearly independent.

8. December 2020 · Q5(c)

   There is no normal matrix having one of the entries as 2.

9. December 2020 · Q5(d)

   If A is positive definite, then A –1 is positive definite.

10. December 2020 · Q5(e)

    Every upper triangular matrix is diagonalisable.

Linear Algebra study material

IGNOU publishes the full MMT-002 self-learning material free on eGyanKosh: every block and unit on jordan canonical form and applications of unitary matrices.