"Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another." (from Wikipedia)
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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.
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.
Linear Algebra is a special "subset" of algebra in which they only take care of the very basic linear transformations. There are many many transformations in Algebra, linear algebra only concentrate on the linear ones. We say a transformation T: A --> B is linear over field F if T(a + b) = T(a) + T(b) and kT(a) = T(ka) where a, b is in A, k is in F, T(a) and T(b) is in B. A, B are two vector spaces.
Well, hello there! Boolean algebra and linear algebra are like two different colors on your palette. Boolean algebra deals with true or false values, like painting with just black and white. Linear algebra, on the other hand, involves operations on vectors and matrices, adding more colors and shades to your artistic expression. Both are beautiful in their own way, just like how every brushstroke adds to the beauty of a painting.
Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.