MMT-002 IGNOU Solved Assignment 2026-27

MMT-002 Solved Assignment: Linear Algebra (TMA 30% Weightage)

This digital PDF solution covers 100% of the official IGNOU curriculum for MMT-002: Linear Algebra, including mandatory blocks and verified reference answers. Below are key syllabus-aligned units with structured breakdowns:

1. Jordan Canonical Form (Block-1)

• Definition and Properties: Detailed derivation of Jordan blocks, nilpotent matrices, and the relationship between minimal polynomials and Jordan forms.
• Computation Examples:
  • Diagonalization vs. Jordanization for a given matrix (e.g., A = [1 1; 0 1]).
  • Proof of A^2 = A implies a Jordan block of size 2.
• Applications: Solving systems of linear recurrence relations using Jordan forms (word limit: 500).

2. Applications of Unitary Matrices (Block-2)

• Unitary Diagonalization: Step-by-step proof for Hermitian matrices (e.g., A = [0 1; 1 0]) and their unitary eigenvectors.
• Spectral Theorem: Verification for normal matrices with explicit unitary matrices U and D.
• Quantum Mechanics Analogy: Brief connection to unitary transformations in state evolution (word limit: 250).

FAQs

Check if the geometric multiplicity of each eigenvalue equals its algebraic multiplicity. If not, the matrix requires a Jordan chain (e.g., J = [λ 1; 0 λ]).

Yes, by the Spectral Theorem, every Hermitian matrix A satisfies A = UDU^*, where U is unitary and D is real diagonal.

Submission Compliance

• Word limits strictly enforced (e.g., 100 words for short-answer proofs, 500 words for derivations).
• Includes Hindi-language solutions (where applicable) for bilingual students.
• Deadline-aligned with current IGNOU academic calendar (check eGyanKosh for updates).