Practice Question on Finding Rank (Q2)

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/GATE-GUIDANCE-BY-SANCHIT-SIR/engineering-mathematics/linear-algebra/rank-of-a-matrix/asset-practice-question-on-finding-rank-q2 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  2. DataBase Management System/DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  6. C Language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics
  10. Theory Of Computation/Automata Theory: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  11. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  12. Engineering Mathematics: Permutation and Combination, Linear Algebra, Calculus, Probability, Statistics
  13. General Aptitude: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Mensuration and Geometry, Mental Ability, Arithmetic, Profit and Loss, Powers and Exponents (Surds and Indices), Average, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, Venn Diagram, Seating Arrangements, Blood Relations, Directions (Direction Test), Analogy, Algebra, Time and Work, Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Cubes & Dices, Ranking, Order and Sequence, Mixture and Alligation, Age Problems, Clock, Selection Decision Table (Decision Making), Data Arrangement
  14. English (Verbal Aptitude): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Direct and Indirect Speech, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Correction (Error Correction), Verbal Analogy (Word Based Analogy), Conjunction, Interjection, Verb, Articles, Adverb, Modals, Sentence Construction
  15. Live Classes Recordings(Earlier Batch): GATE 2026 Live Class
  16. Full Mock Test:
  17. Previous Year Papers:
  18. GATE 2026 Counselling: Counselling and Guidance Sessions
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture focuses on determining the rank of a matrix using row reduction techniques in linear algebra. The instructor begins by reviewing determinant formulas for 2x2 and 3x3 matrices before moving to a specific 4x4 matrix problem. The core task is to find the rank, which involves transforming the matrix into row echelon form to count the number of non-zero rows. The instructor demonstrates elementary row operations, such as swapping rows and subtracting multiples of one row from another to create zeros below pivot elements.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card "LINEAR ALGEBRA" followed by formulas for determinants. The instructor introduces a 4x4 matrix problem labeled "Q2" with the instruction "find rank?". He writes the initial matrix on the whiteboard, which contains values like 1, 4, 8, 7 in the first row. He performs a row swap operation, denoted as $R_2 \leftrightarrow R_3$, to position a non-zero element in the second row. He then sets up further operations: $R_2 \leftarrow R_2 - 4R_1$ and $R_3 \leftarrow R_3 - 3R_1$. He begins calculating the new entries for the second row, specifically focusing on eliminating the first element.

  2. 2:00 – 4:12 02:00-04:12

    The instructor continues the row reduction process. He calculates the new second row by subtracting 4 times the first row from the second row, resulting in zeros in the first column. He similarly processes the fourth row. The resulting matrix is displayed with zeros in the lower left triangle. He identifies the pivot elements, marking them with stars or circles to highlight the leading non-zero entries. By counting the non-zero rows in the echelon form, he determines the rank is 3. He draws a generic matrix with stars to visually reinforce the concept of rank as the number of linearly independent rows. Finally, he circles the pivot columns in the original matrix to show which columns are linearly independent.

The lesson effectively bridges theoretical definitions with practical application. By starting with basic determinant formulas, the instructor sets a foundation before tackling the more complex task of finding the rank of a 4x4 matrix. The step-by-step row reduction demonstrates how to systematically eliminate variables to reach row echelon form. The visual aids, such as circling pivots and drawing generic matrices, help clarify that rank corresponds to the number of non-zero rows or linearly independent columns. The final conclusion of rank = 3 is derived directly from the transformed matrix structure.

Loading lesson…