Life and Gaussian Elimination

Given a set of equations, we are required to find out the value of x1,x2,x3,x4. For example, the 4 equations below


2x1 + 2x2 +x3 - x4=1

0x1 - 2x2 -3x3 + 4x4=0

0x1 + 0x2 +x3 - 2x4=3

0x1 + 0x2 +0x3 + 2x4=2



They can be expressed in a matrix form, known as the augmented matrix as follows by placing their coefficients in it:



[2 2 1 -1 l 1 ]
[0 -2 -3 4 l0 ]
[0 0 1 -2 l 3 ]
[0 0 0 2 l 2 ]



By right, the equations are not as nice as this, but for examples sake I have made it in this manner. We are supposed to perform ROW operations to an augmented matrix, where by we can either:



1. Interchange Rows

2. Multiply the rows by a scalar

3. Adding a multiple of another row



The final matrix obtained as shown above is in what we call echelon form. This means whatever is underneath the diagonal of the top left term MUST be zero. So before performing the row operations, things may not be as simple as it looks.



From there we can associate it with the initial form of equations, and we can derive values of x1,x2,x3 and x4.



From the backsubstitution, we can see that



2x4 = 2

x4 = 1.



x3 - 2x4 =3

x3 -2(1) =5

x3 = 7



-2x2 - 3x3 + 4x4 = 0

-2x2 - 3(7) + 4(1) = 0

x2 = -17/2



2x1 + 2x2 + x3 - x4=1

2x1 +2(-17/2) +7 - 1 = 1

x1 = 6



And there you have it, the answers.

In every single one of us, there is a market value. With that value, we work ourway UPWARDS together with other people with other values. However, we cannot confirm plus guarantee plus chop stamp that ultimately, the people in the equation are a PERFECT combination to the end result. Some of us are a 'plus', some of us are a 'minus' and the math just adds up to see if eventually you as a team eventually make a positive or negative impact to society. So what if you are able to work well in a group of 2 or 3? Yes, your overall output as a team maybe positive, but in a group of say 4 or 5, your net gain is in the red and you are heading for bankruptcy.

Now comes the contradictory part. 'But when you bring over the minus value, it becomes positive what! so all the more we should be negative, relax and skive all the way! shiok leh!' Yes it is true that when you bring over the minus sign it becomes a plus because other people's large value negates your weakness. Nonononono. Nobody is perfect and everyone has their negatives and restrictions. There is a limit to everyone's mental, emotional, physical capability. In other words, there is a negative deficit in everyone, in some way and some how. Why do people think so highly of themselves? Pride, ego, etc. So they are definitely most likely to put themselves as a positive value.

BUT the beauty of math is, when we cross over the equals sign, (which I felt looks like the straight and narrow way "=" we are in fact taking on a PLUS sign with us.

I.e. to say. We are crossing over to the world via the narrow way, taking Christ together with us, to make a POSITIVE impact eventually.

Which directly implies that every. single. one. of. us. is. a. solution.


WOW.


'Then how about the positive people?" Oh. What to do. Conversely it is the same principle. Carrying over pride will definitely not bring you anywhere. What makes you that you can walk into any company demanding a 10k salary plus car plus house plus allowance? Pride. So which brings me back to the title, what exactly are we eliminating? Yup no money for you guessing it right. Pride.


I'm not sure if people are catching anything from the whole chunk, but I know for sure as I'm typing this, I am.