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Linear algebra is used to analyze systems of linear equations. Oftentimes, these systems of linear equations are very large, making up many, many equations and are many dimensions large. While students should never have to expect with anything larger than 5 dimensions (R5 space), in real life, you might be dealing with problems which have 20 dimensions to them (such as in economics, where there are many variables).
Linear algebra answers many questions. Some of these questions are:
How many free variables do I have in a system of equations?
What are the solutions to a system of equations?
If there are an infinite number of solutions, how many dimensions do the solutions span?
What is the kernel space or null space of a system of equations (under what conditions can a non-trivial solution to the system be zero?)
Linear algebra is also immensely valuable when continuing into more advanced math topics, as you reuse many of the basic principals, such as subspaces, basis, eigenvalues and not to mention a greatly increased ability to understand a system of equations.
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Is linear algebra and linear equations the same?
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.
Are calculus and linear algebra courses hard for an individual who got an a plus in algebra?
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.
What is the difference between algebra and linear algebra?
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.
What is linear algebra?
"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)
How Boolean algebra is different from linear algebra?
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.
