# Learning Mathematics for IIT JEE

## Sunday, May 8, 2016

### XII - 11.24 Solution of a homogeneous system of linear equations - Video Lectures

Solving a Homogeneous System

NightingaleMath

__________________

__________________

### XII - 11.23 Rank method - Video Lectures

9 May

A number r is said to be the rank of a an "m x n" marix if

i) every square sub matrix of it of order (r+1) or more is singular, and

ii) there exists at least on square matrix of order r which is non-singular.

In other words, the rank of a m x n matrix is the order of the highest order non-singular square submatrix of it.

Solving 4x4 Linear Equations by Rank of Matrix Method_Detailed Step by Step Explanation

Sujoy Krishna Das

__________________

__________________

A number r is said to be the rank of a an "m x n" marix if

i) every square sub matrix of it of order (r+1) or more is singular, and

ii) there exists at least on square matrix of order r which is non-singular.

In other words, the rank of a m x n matrix is the order of the highest order non-singular square submatrix of it.

Solving 4x4 Linear Equations by Rank of Matrix Method_Detailed Step by Step Explanation

Sujoy Krishna Das

__________________

__________________

### XII - 11.22 Solution of a non-homogeneous system of linear equations - Video Lectures

9 May

Non-Homogeneous system of equation with infinite solution

Rahul Abhang

_______________

_______________

Nonhomogeneous System Solutions

TheTrevTutor

_______________

_______________

Non-Homogeneous system of equation with infinite solution

Rahul Abhang

_______________

_______________

Nonhomogeneous System Solutions

TheTrevTutor

_______________

_______________

### XII - 11.21 System of simultaneous linear equations - Video Lectures

Consistency of a System of Linear Equations

MathDoctorBob

__________________

__________________

Consistent And Inconsistent System of Equations Example - 1 / Matrices / Maths Algebra

We Teach Academy Maths

__________________

__________________

### XI - 2.4 Some results on relations - Video Lectures

1. If R and S are two equivalence relations on a set A, then R∩S is also an equivalence relation on A.

2. The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

3. If R is an equivalence relation on a set A, the R

Proof of Set operations in Relations -1 / NCERT Std XI Mathematics

MathsMynd

________________

________________

2. The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

3. If R is an equivalence relation on a set A, the R

^{-1}is also an equivalence relation on A.Proof of Set operations in Relations -1 / NCERT Std XI Mathematics

MathsMynd

________________

________________

### XI - 2.5 Composition of relations - Video Lectures

When r and S are two relations from set A to B and B to C respectively, we can define a relation SoR from A to C such that

(a.c) Є SoR imples for all b Є B subject to the relations (a,b) ЄR and (b.c) ЄS.

SoR is called the composition of R and S.

Properties of SoR

In general RoS is not equal to SoR.

(SoR)

^{-}= R

^{-}oS

^{-}

^{}

Composition of relations

Math 290, GMU

^{}__________________________

__________________________

### XII - 11.20 Echelon form of a matrix - Video Lectures

Elementary Linear Algebra: Echelon Form of a Matrix, Part 1

James Hamblin

____________________

____________________

Subscribe to:
Posts (Atom)