you don't go from algebra to calculus and linear algebra. you go from algebra to geometry to advanced algebra with trig to pre calculus to calculus 1 to calculus 2 to calculus 3 to linear algebra. so since you got an A+ in algebra, I think you are good.

yes, also this question belongs in the linear algebra forum not the abstract algebra forum

Linear algebra is restricted to a limited set of transformations whereas algebra, in general, is not. The restriction imposes restrictions on what can be a linear transformation and this gives the family of linear transformations a special mathematical structure.

Lis - linear algebra library - was created in 2005.

Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.