MATLAB -> MATrix LABratory -- of course it uses matrices! Even a simple variable is treated as a 1x1 array.
No, MATLAB isn't just for matrix math, you can even do a bunch of calculations from the command window. Values that you set are saved in the Workspace window. So, you can define variables and save/change their values and chain as many commands as necessary to calculate some result. But you really don't want to do that for anything other than the most trivial calculation.
You really want to create a script because, when it doesn't work, you can edit just the offending lines of code and run again. Using the command line, you may need to reiterate several steps to get intermediate values before getting the final solution.
A long time ago ('88), I was involved with the design of a semiconductor plant. I wanted to verify pipe sizing on the Deionized Water branch and return lines by assuming certain flows to drain (water leaving the system) and certain flows to return. Water must remain above 100 fpm in all pipes and so on. This is across the entire production floor, in all the aisles. Hundreds and hundreds of feet of pipe and I have forgotten how many branches but it seemed like a lot.
I modeled the system in Excel and got it to balance in two iterations. I don't recall how I did it but I'm guessing "Method of Residuals" that was taught in grad school for heat transfer from a hot spot. All part of a required Numerical Analysis course.
In any event, it worked, the flows were correct, the return pipe was necessarily smaller than the supply pipe and so on.
In thinking about it today, it isn't unlike a bunch of parallel branches containing a series of resistors with an applied voltage and solving for currents (flow rate). I didn't think of that at the time... The point is, Excel was a matrix and this was a matrix problem. Each cell was an element of a much larger matrix.
You just never know when these tools will be exactly the thing you need. Of course, things were a little more limited 30 years ago.
One thing that comes up in MATLAB is creating a matrix where one wouldn't think. Consider plotting a sine wave: All we need is a series of points to plot as a function of x: y=sin(x). So, I give sin a value for x and it returns the sin(x). If I give it a bunch of values, I get the results that should be a sine wave.
MATLAB just about forces you to make x a vector of values, as many points as you want in the result. Then sin(vector x) returns a similar vector of sin(x) values and we plot the vector x and y for as many points as are in the original x vector. In Fortran, we would step through a bunch of values, in MATLAB, the values are already in the x vector. C would also be step by step and C++ would hide everything in a class.
Here is a little sine wave example. Note how few lines of code are required and how the fact that x and y are vectors doesn't even come up. That single statement y=sin(x) is magic! In one line of code we took values of x, all 101 of them, took the sin of x and stuffed the values in the y vector - all 101 values.
Don't let vectors and matrices be some kind of bug-a-boo. They are a natural way of expressing certain operations.
If you get into Kirchhoff's Laws, you will be doing matrix arithmetic to solve several equations in several unknowns. You can solve directly with MATLAB/Octave or by hand using row reduction. Here's a video and there is a part 2 to go along with it.
https://youtu.be/9LYVi-n-6JwThis stuff may be tedious but it isn't hard.
x=0:2*pi/100:2*pi; % create vector x with values of 0 to 2*pi and
% 100 intervals - 101 elements
y=sin(x); % create vector y with values y(x) = sin(x)
% 101 elements - computed in a blink of an eye
plot (x,y) % plot the curve
ylabel('Sine Function') % label the Y axis
title('SIN(x)') % add a title
axis([0 2*pi -1.5 1.5]) % set the x and y axis limits
shg % show the graph
% notice how the x axis runs from 0 to about 2*pi
% and the y axis runs from -1.5 to +1.5
I forgot the output plot, now attached