Solving Linear Equations by Row Echelon (stair Case shape) Technique
Conventional method of solutions become more difficult as the number of variables and its equations increase.
The method of using rows and columns with simple rules provides the shortcut to the conventional method.Strictly speaking,it is not algebra or mathematics but a tool(or a trick) to get the results in easy steps.
However you must understand the notations , definitions and its meaning interpret the results in the same way as you find the solution in the conventional way.
Again these notations are a short hand mnemonic for a long statement of a mathematical/or operational description in words.
SO YOU MUST UNDERSTAND THE INNER MEANING OF THE NOTATIONS THOROUGHLY TO BE ABLE TO USE IT FREELY IN THE FLOW OF THE RESULTS FRO A SOLUTION STEPS.
The math behind the notations and shorthand-words is generally very simple and intuitive.
This is the first video.
The method of using rows and columns with simple rules provides the shortcut to the conventional method.Strictly speaking,it is not algebra or mathematics but a tool(or a trick) to get the results in easy steps.
However you must understand the notations , definitions and its meaning interpret the results in the same way as you find the solution in the conventional way.
Again these notations are a short hand mnemonic for a long statement of a mathematical/or operational description in words.
SO YOU MUST UNDERSTAND THE INNER MEANING OF THE NOTATIONS THOROUGHLY TO BE ABLE TO USE IT FREELY IN THE FLOW OF THE RESULTS FRO A SOLUTION STEPS.
The math behind the notations and shorthand-words is generally very simple and intuitive.
This is the first video.
You will frequently here some terms and have to use them liberally in making worded statements in in linear Algebra.
Some of them are ! Linear Combinations,Set of..,Column Vector and Row Vector,Vector Space,Span of Vector,(More to add progressively)
Vector Space:
It is not to do less with 2D or 3D but with fulfilling the mathematical property of vectors and additional stipulations of a problem(if any)..
Addition-Scaling(simple multiplication by #)-Commutative(switch/swap)-Distributive( of brackets)-
VECTOR SPACE VIDEO
MATRIX(A) decompositio by LU
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