Taking Linear Algebra... Doing the problems just fine but not really understanding the deeper meaning...

Coordinate systems in more than 2 dimensions. It's how the real world is measured!

Age or stage structures population growth.

Any system of equations. Like building a bridge, water transporting a contaminate (sometimes more difeq) lots if things.

It is a puzzle, as linear algebra. You just use the puzzle to find the answer

Think optimization buddy. And then think about why optimization analysis is less important now than 40 years ago when computers were slow and not readily available. Do the the math, get a good grade and move on unless you want to make it your life's work.

It felt that way for me a little bit at first when I was overwhelmed with all of the new definitions, but eventually things came together. You'll have to give more information or some examples if you want further feedback/advice.

I generally think of matrices as functions on vectors. What makes them useful is that they follow certain rules and constraints that make them easy to manipulate.

You don't need any of that. Science is from a Muslim priest in Iran 1000AD.

Watch the 3blue1brown linear algebra videos that can be found on YouTube. These may help to build some geometric intuition.

math prof wrote:

Watch the 3blue1brown linear algebra videos that can be found on YouTube. These may help to build some geometric intuition.

Really great answer. What a service to humanity!

i wouldn't really worry about it at this point unless there something's specific that's puzzling you. there's a lot to learn.

linear algebra is one particular flavor of mathematics that you'll eventually bump into wherever you need math. if calculus is the language of change, then linear algebra is the language of space. abstract algebra is language of relationships (or mathematical operations). topology and metric spaces are the language of shapes.

because mathematical objects in general have all of these properties, you'll eventually discover that all these areas sort of converge. so just keep plugging away. you have to start somewhere.

oh, and linear algebra courses are often used for exposing students to discrete math (writing proofs etc.) so you'll find that some linear algebra is really focused on solving equations and doing stuff with matrices etc. and some is more theoretical and based on linear transformations, vector spaces. etc. You might start at either end of the spectrum, or somewhere in the middle.

good luck

I can advise you to use different techniques for the development of logical thinking. You can use YouTube as an educational platform for visualizing complex algebraic manipulations. This method is suitable for people who do not visualize well. The second way is to use specialized resources https://plainmath.net/secondary/calculus-and-analysis/precalculus/composite-functions with detailed descriptions and conclusions. I recommend combining these methods because a person is able to generate his own vision of decisions through the synthesis of other people's opinions.

dumbassMF wrote:

It's a lot like religion, lots of repetition and memorization, but no deeper meaning...

It's the complete opposite of religion.

Religion never built a nuclear weapon. Solving linear equations was useful in doing so.