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What are real life situations which are applications of linear equations?
Cell phone companies
When will you use algebra in real life?
You could use algebra in real life in nearly anything that you do. You could use algebra to calculate how much gas you will put in your car and how much it will cost you.
What are some real life applications of abstract algebra?
By definition, none. For if it did have real life applications it would not be called abstract! +++ You could consider it as establishing the rules by which the algebra needed to perform real-life tasks works. For a simple example, if C = AB then you could say, "Fine, suppose we call A and B the sides of rectangle than C is its area, OR if we call A and B speed and time respectively then C is the distance travelled. In both cases the algebraic rules are the same: multiply two values and you obtain their product; but many practical applications are in fact simple products so there we have the underlying pure algebra for solving them. And from that we can use pure algebra rules to determine A or B from the others.
What math comes after calculus?
Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.
Does the range of linear equations have all real numbers?
No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.
