VTU 2022 Scheme  ·  Degree  ·  CSE

Linear Algebra BCS405D

Module-wise notes, PYQs, and a built-in resource explorer — everything you need to crack BCS405D in one focused page.

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CodeBCS405D
Credits03
CIE / SEE50 / 50
TypeTheory
Exam3 Hours
Hours / Week2:2:0:0
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Last Updated:  15 March 2026

Module Overview

M1

Module 1 Overview

Introduction, Vector spaces, Subspaces, Linear Combinations, Linear Spans, row space and column space of a Matrix, Linear Dependence and Independence, Basis and Dimension, Coordinates.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

M2

Module 2 Overview

Introduction, Linear Mappings, Geometric linear transformation of i2, Kernel and Image of a linear transformations, Rank-Nullity Theorem (No proof), Matrix representation of linear transformations, Singular and Non-singular linear transformations, Invertible linear transformations

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

M3

Module 3 Overview

Introduction, Polynomials of Matrices, Applications of Cayley-Hamilton Theorem, Eigen spaces of a linear transformation, Characteristic and Minimal Polynomials of Block Matrices, Jordan Canonical form.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

M4

Module 4 Overview

Inner products, inner product spaces, length and orthogonality, orthogonal sets and Bases, projections, Gram-Schmidt process, QR-factorization, least squares problem and least square error.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

M5

Module 5 Overview

Diagonalization and Orthogonal diagonalization of real symmetric matrices, quadratic forms and its classifications, Hessian Matrix, Method of steepest descent, Singular value decomposition. Dimensionality reduction - Principal component analysis.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

Resource Explorer

Browse all BCS405D study materials — notes, PYQs, and revision resources. Navigate folders for module-wise content and preview files before downloading.

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Frequently Asked Questions

What is BCS405D (Linear Algebra BCS405D)?

Linear Algebra BCS405D is a VTU course covered through module-wise syllabus, notes, and PYQ-driven exam practice available on this page.

How many credits is BCS405D?

Credits for BCS405D: 03.

Are notes and previous year question papers available for BCS405D?

Yes. You can access organized notes, PDFs, and PYQ material from the file explorer/resources section on this page.

How should I prepare Linear Algebra BCS405D for VTU exams?

Start with module summaries, solve recent PYQs unit-wise, and finish with complete paper practice under time constraints for SEE readiness.

Is this BCS405D page updated for current VTU scheme?

Yes, this page is maintained with current scheme-oriented materials and practical exam-focused resource curation.

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