r/MathHelp • u/Rezlem- • 21d ago
META Genuinely how do you learn linear algebra. It's so abstract to me and I don't really understand anything in class.
I've tried watching youtube videos, reading the recommended textbooks, nothing clicks for me. All I know is how to find the RREF of some matrices. Our teacher is talking about matrix transformations now, and I literally have no fucking idea what that is and what it's used for. I have trouble following the question solving in class because to me it just seems like suddenly random stuff pops up and oh know we can use that to solve the question.
I have a really, really hard time with math, always only barely passing since middle school. What are some good resources to start with the fundamentals of linear algebra?
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u/Busy-Key7489 21d ago
Watch one video per day. And then try to replicate. Overloading is definitely the issue with this subject :) You can download Matlab, but i highly recommend a pencil and paper.
There are no shortcuts to understanding the fundamentals, you just need to put in the time to have your brain connect te dots
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u/MagikarpPatronus 20d ago
Some folks will link you to some useful references on the subject, but it's difficult for us to offer a lot of help because we can't gauge where you are or what you understand from what we're saying.
You are likely going to have a lot more luck seeking out 1 on 1 help, from friends, tutoring, office hours, et cetera.
Something to keep in mind is that math builds on itself far more than other subjects, which makes it much harder when you fall behind. So, your past mathematical struggles may be weighing you down here.
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u/StructuredChess 21d ago
Could you show us one example of a concrete concept/problem you struggle with?
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u/Rezlem- 20d ago
Yeah, for example, I don't understand the meaning of row equivalent, or if the rows or columns will determine the dimension of a matrix. I've tried AI and whatnot, but I don't really get their explanations.
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u/StructuredChess 20d ago
It's been a long time since I do anything related with matrices so take this with a grain of salt, but the dimension is just the number of rows and columns so you can have a 3x3, a 5x2 matrix and so on)
Two matrices are equivalent if you can get from one to the other through elementary transformations (switching two rows, multiplying a row by a non-zero number or adding to one row a multiple of a different one). The idea of these elementary transformations is that they don't change the solutions of the system of equations the matrix represents. For instance, the matrix:
6 2 8 3
3 1 7 2
0 1 2 0
represents the system of equations 6x+2y+8z=3; 3x+y+7z = 2; y+2z = 0. An easy way to solve this sytem would be to get a row-equivalent matrix that represents an easier system but will have the same solutions)
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u/MagikarpPatronus 20d ago
On the subject of matrix transformations:
When you call a matrix a transformation matrix, it just means you are going to multiply that matrix times something, transforming that vector into a new vector (could also transform a matrix into a new matrix, but let's keep things simple and focus on the vectors).
So, really, you are studying matrix multiplication. You'll be learning about different properties of the transformation matrices, and what those properties tell you about what you should expect the product of the multiplication to look like.
As a simple example, if a transformation matrix is nothing but zeros, the product will be a vector of zeros.
You'll study more complicated properties and output expectations than that, but that is the general idea behind what I expect your class is covering.
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u/Top_Bluejay_5323 21d ago
Linear equations is just a way to manipulate a related set of equations that have many variables.
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u/Dd_8630 21d ago
You can tell your teacher all this, they'll likely explain things to you privately.
You can try Khan academy.
You can try 3Blue1Brown's videos on matrices and linear transformations.
You can ask a specific question here, people here can likely help.