Lecture 2 Algebra in Matrices | Engineering Mathematics | Matrices & Determinants | JUT Ranchi

Описание: 📘 Chapter 1: Matrices & Determinants – Lecture 1.2
🔢 Algebra of Matrices | Addition, Subtraction, Scalar Multiplication & Matrix Multiplication Explained

Welcome to this detailed and student-friendly lecture on Matrix Algebra!
In this video, we dive deep into the mathematical operations performed on matrices — the foundation of higher mathematics, engineering, computer science, data science, and more.

🔍 What You Will Learn in This Lecture
➕ 1. Matrix Addition

Condition for addition

Adding corresponding elements

Step-by-step solved examples

➖ 2. Matrix Subtraction

When subtraction is possible

Element-wise subtraction

Solved examples for quick understanding

✖️ 3. Scalar Multiplication

What is a scalar?

How to multiply a matrix by a constant

Real-life examples & applications

🧮 4. Matrix Multiplication (Most Important!)

Condition: Columns of A must match rows of B

“Row × Column” method explained in a very easy manner

Multiple solved examples (2×2, 2×3 × 3×2)

Clear explanation of each element of the product matrix

⚠️ Important Matrix Properties Covered

Matrix multiplication is NOT commutative (AB ≠ BA)

Associative law holds → A(BC) = (AB)C

Distributive law → A(B + C) = AB + AC

Identity matrix property → AI = IA = A

Zero matrix multiplication → A·O = O

📝 Quick Revision Table in the Lecture
Operation Condition Method Resulting Order
A + B Same order Add elements Same as A, B
A – B Same order Subtract elements Same as A, B
kA No condition Multiply each element Same order
AB Col(A) = Row(B) Row × Column (Rows of A) × (Cols of B)
🎯 Why This Lecture Is Important?

Matrix operations are used in:

Solving systems of linear equations

Computer graphics & 3D animations

Machine learning & data science

Economics & optimisation

Engineering (especially civil, mechanical, CS, electrical)

Mastering these basics will make the advanced chapters very easy!

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