Gato_Solo said:
Examples. We need examples.
You're a carpenter or contractor, take your pick. You need to put in a staircase that goes up 10 feet, with a minimum land of 10" per step and a maximum rise of 6" per step (guessing here, I don't know what building codes stipulate).
You need to know what total length the staircase will occupy so you can see if it will fit, and know where to start with the supports.
R = maximum rise
H = height of staircase
l = minimum land
L = total length of staircase
L = (H/R)*l
Yeah, simple example, and most people would do the problem in smaller steps instead of just one equation... but it's still algebra. People use algebra when they think they're just "adding and subtracting" and don't realize it.
Like I said though, linear algebra (vector algebra, matrix mechanics, whatever you want to call it) is less generally useful. Not many people need to find the subset of a given space.
I use it occasionally at work since the finite element method relies on manipulations and solutions of matrices, but even then it's just the most basic operations.