Whatever you've heard, matrices are not your friend. Unless you're some kind of math major, in which case you wouldn't be here right now. So I can safely say that matrices are not your friend. Mine neither. On the bright side, though, if just memorize how to plug and chug your way through each type of matrix problem that your class does, you'll be okay. Just don't ask why any of this stuff works - especially Cramer's Rule - because I have no idea!
Btw, you'll notice I used the words "that your class covers" in the paragraph above. That's because teachers vary a lot in what matrix stuff they cover, but everything I've seen is below, so hey. (There's a good chance you'll have to do most of it: the question marks would be solving systems, either with Cramer's Rule or Row Operations.)
Basic Matrix Operations
This video covers the most basic things you can do to matrices which are the same size: adding and subtracting them. We'll also learn how to multiply them by a scalar, which is another word for constant.
To multiply matrices they don't have to be the exact same size, but they do have to obey certain guidelines that I cover in this video. I'll also take you through the tedious process of actually multiplying them, which involves multiplying a row of the first matrix by a column of the second in what's basically a glorified FOIL technique.
In this video we'll cover how to calculate the determinant of 2x2 and 3x3 matrices, the latter requiring you to break the 3x3 into a bunch of 2x2's. If your teacher lets you use calculators for 3x3's, you're in luck; otherwise you're going to get tired of me telling you not to forget the minus sign in front of the second term!
You've known for while how to solve a system of equations using elimination or substitution. But if you get tired of those, welcome to Cramer's Rule, which uses matrices and determinants to solve for x, y, and any other letters you've got!
Inverse & Identity Matrices
The identity matrix is the one - either 2x2, 3x3, or 4x4 - with a diagonal of 1's and everything else 0's. What's it got to do with inverse matrices? If you multiply a matrix by its inverse, you get the identity matrix, kind of like if you multiply a function by its inverse you get x.
Solving Systems: Matrix Row Operations (Gauss Jordan or Gaussian Elimination)
This is a slow and tedious way of solving systems, but then again, what isn't? In this rather long video we'll solve a system of 2 equations 2 unknowns, and 3 equations 3 unknowns. elimination, substitution and Cramer's Rule are all better choices.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)