They are not alternative solutions so that we can compare them.
Relational database (which is based on relational algebra) demands (atleast the founder of relational database Codd suggests) that the query language follow linear syntax. The linear syntax languages don't rely up on newline characters as terminators of expressions or statements -- instead they rely on other tokens such as semicolon or comma and so on.
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Linear algebra concerns vector spaces whether finite- or infinite-dimensional. Abstract algebra, or modern algebra, includes linear algebra, along with many other kinds of objects, such as groups, rings, fields, lattices, and so on. In part, it was an attempt to put mathematics on a more rigorous footing. Please see the links.
Example: Algebra will show you how quickly the gallon will fill over time. Calculus will show you how quickly the gallon will fill over time while it is also being slowly drained.
linear
Linear means a straight line.
Nonlinear do not satisfy the superposition principle. Linear problems, as implied, do.