Why is Linear Algebra Important and How is it Applied?

[thharrimw]

i'm just starting linear algebra and I've gone over the basics of matrixes (ex. inverces, LU decompsition, basic operators, and how to solve basic systems of equations) but i don't know why it is really important to know linear algebra so far everything I've done i could do in basic algebra in some cases i can see where is would be simpler to use linear algebra and linear program but i just was wondering what are some appelacations of linear algebra?

 

[HallsofIvy]

The theory of linear differential equations is based on Linear Algebra.

 

[thharrimw]

The theory of linear differential equations is based on Linear Algebra.

what is the throry of linear differential equations? i know what Differential Equations are and i know what linear equations are but I'm uncleer on what linear differential equations are.

 

[maze]

Ok, here are a few simple questions that linear algebra can easily deal with. Perhaps one will pique your curiosity.

If you have a plane in 3D space and a point p not on the plane, what is the shortest distance from p to the plane? What about a point and hyperplane in 4D space? 5D? 100D?

Can you find a closed form expression for the nth term of the fibonacci sequence, f(n)? The fibonacci sequence is 1 1 2 3 5 8 13 21 ... where f(n) = f(n-1) + f(n-2).

In 2D, if you flip an object about 2 different lines in succession, it is the same as doing a single rotation and no flips. Why is this? Is the same thing true for higher dimensions?

If you have a function f(x), what are the constants a0, a1, a2, ..., an such that the polynomial a0 + a1*x + a2*x^2 + ... + an*x^n gives the best approximation of f(x)?

 

[thharrimw]

this may be a dum question but are the varables x, x^2, x^3 and so forth the higher dimensions that you are talking about? and how would you use linear algebra to do ressions? right now I'm learning how to find det(A) so where dose that fit into the bigger picture of linear algebra?