The other responses to your question are classic mathematicians giving math answers to someone who doesn't see why the math is useful in response to asking why

The other responses to your question are classic mathematicians giving math answers to someone who doesn't see why the math is useful in response to asking why is the math is useful. The most straightforward application is solving systems of equations. From early high school, we have problems like x+y=2 and x-y=3 and are asked to solve these. We then add a z (and maybe a w) and solve systems of 3 (or 4) equations before realizing it gets annoying very quickly. Linear algebra is simply the generalization of solving these equations. Instead of writing out all those equations line by line, let's make a new notation as: [[1,1],[1,-1]] @ [[x,y]] = [[2,3]] @ is of course matrix multiplication but what it does does not really matter. Only that it performs some "function". But is this notation helpful? It turns out this function is really useful to answer other questions. From here, we can go on to show very interesting things like how to find the answers for x and y. It turns out that it has a recursive process similar to when solving it by hand (isolate one of the variables, plug into another equation, isolate another, ...) and part of this recursive process has a pattern we will call the determinant. Turns out that when the determinant is 0, funny things happen. The point is that it all started by trying to solve these equations which are interesting from a mathematical point of view but also show up naturally in many business applications. See Leontief's Model [1] for how this could be useful. Consumption equals production and bills being linear (#apples * $apples + #bananas * $bananas + ... = total spent) make linear systems arise naturally. All the things that come later, eigenvalues, SVD, etc. were all discovered as mathematical curiosities and later realized that they had very useful applications such as solving OLS and compression. [1] - https://www.math.ksu.edu/~gerald/leontief.pdf https://www.math.ksu.edu/~gerald/leontief.pdf