Linear Algebra Notation
System of Sentences
The language of mathematics is equations → These in linear algebra can be taught of as sentences!
System of sentences behaves alot like system of equations. Lets look at some examples
Non-Singular System → A system that carries as many many pieces of information as sentences
Singular System → That does not carry as much info as sentences → Less informative than a non-singular one
System of Linear Equations
We can extract numerical information from sentences and solve them as a system of equations.
For example:
If you were to do a little re-arranging and subbing in, you can see that one banana costs $2, and apple costs 8 dollars.
We can also graph this relation, and you can see the two equations intersect at the solution!
Be-careful of REDUNDANT information!
The solution to this system is… infinitely many, as many combinations work!
We can also see this geometrically!
There can be systems with NO solutions aswell, as the system has a flaw. i.e. the system has a contradiction → i.e. one equation saying dog is black, another equation saying dog is red
We can see this geometrically, as the two lines
Summary of the examples:
System of Equations as Lines
To graph the equations a+b = 10 and a + 2b = 12, try to think of what happens when yaxis = 0, or xaxis = 0, or some numbers that make the equation true before you go ahead and connect the dots w/ the line
Mathematically, you can also solve it using y=mx+b, or using slope and the intercept
Geometric Summary of the 3 types of outcomes of linear systems of equations
