CAN LINEAR ALGEBRA DESCRIBE THE WORLD?

Background


1. The Singular case in Linear Algebra.

When you have a system of equations in two dimensions. If the two lines are
parallel, the two lines have the same slope and they do not intercept. The
tow lines are increasing or decreasing, depending on their slopes, at the same
rate of change.
If we use a table of values from a linear equation, we can see this rate of change by observing the values of y and of x, as they increase or decrease. Sometimes the lines are increasing by two, by four, etc. If increasing by two then the line have a slope of two, if increasing by four, the line have a slope of 4 and so on.
In linear Algebra when two lines do not intercept the system is said to be singular. This word here
"singular." Was the one giving me the most trouble. Finally, I understand it with perfection.
In 3D,  you not only have the case when two lines are parallel (actually two parallel planes). You also have other cases. Thesingular case increases with the number of dimensions increases. This is only a natural consequenceas with most things in existence, the level of complexity increases with as we move from a simple case to the more robust case.

2. The Vector case.

When I was in college I learned about vector addition and scalar multiplication. Back then I did not
know what was going on. I used to get so confused, when they talked about Linear Combinations and Unit vectors.
Well finally I have begun to understand that if you have any vector whatsoever in 2D for example, that is a point in the
coordinate plane. that is a (2,4) as an example, you not only have the coordinates of the point, but also, and very but very elegantly, a line from the origin to the point. Thus, we can thing about any point in two, three, fourth, etc. points in space forming a unique line, or vector from the origin. What a revelation!!!!