Sunday, May 8, 2016

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


Solving a Homogeneous System
NightingaleMath
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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
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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
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Nonhomogeneous System Solutions
TheTrevTutor

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XII - 11.21 System of simultaneous linear equations - Video Lectures




Consistency of a System of Linear Equations
MathDoctorBob
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Consistent And Inconsistent System of Equations Example - 1 / Matrices / Maths Algebra
We Teach Academy Maths
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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-1 is also an equivalence relation on A.



Proof of Set operations in Relations -1 / NCERT Std XI Mathematics
MathsMynd
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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 
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XII - 11.20 Echelon form of a matrix - Video Lectures


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