Linear algebra is a difficult math subject as any other mathematics course. What makes linear algebra different is, that it is based on certain groups or topics that you should be prepared for in any other circumstances that we are going to talk about in our article today.
In our post, we’re going to discover the 7 crucial and critical reasons why linear algebra is one of the most difficult mathematics courses in college.
so keep reading if you are interested in studying or succeeding in this topic.
1 -it requires being good at geometry
The first concept that students struggle with in linear algebra is the weak foundations they have acquired in their high school courses, especially in geometry.
In linear algebra, you will be using the basics you have studied in your first algebra course Algebra 1, and in the geometry course.
In linear algebra, there will be a lot of vectors and representations that students should do. for instance, you would be required to:
So the first and the most interesting thing to do is to revise some geometry topics, especially high school trigonometry which fundamentally reflects their level in Advanced algebra courses like linear algebra
2 – matrices
Matrices are the number one topic including algebra after vectors. Students study matrices to make operations that simplify vectors of matrices. This is not an easy subject to absorb. It requires a lot of hard work and a lot of people face hardships on it.
matrices become confusing when we try to solve a complex linear algebra problem that has a lot of variables. For instance, solving systems are matrices that have more than 3 variables like in the example below:
In order to solve these kinds of matrices, it will require good maturity in math and solid Basics algebra, especially polynomials.
But the worst thing that makes some people hate linear algebra or exactly matrices is the ability to make mistakes depending on a lot of condensed numbers and signs from tons of calculations you have to make.
It is so stressful especially when students pass exams and have a lot of questions to complete. They have to pay a lot of attention to avoid making mistakes and matrices.
for instance, getting a wrong result of a matrix determinant means that the following responses to questions related are going to be totally wrong.
3 – having solid basics in trigonometry
Trigonometry makes a lot of students suffer and consider linear algebra the toughest subject they have to complete because a lot of topics of linear algebra require a solid foundation in trigonometry, especially trigonometric functions like SIN and COS.
The simple example of trigonometry is used when you try to make a product between two vectors which finally ends up with the following equation.
In addtion, you’ll be dealing with inverse trigonometric functions like Arccosine and arcsin to finally determine the angles between vectors.
Trigonometry is important not only in linear algebra but also In calculus courses. for this reason, they include it in precalculus courses according to its importance in all mathematics College subjects.
4 – It requires solid basics in polynomials
One of the reasons that could be responsible for making you suffer in linear algebra and having weak basics in algebra courses is polynomials.
polynomials are so important to solve systems of matrices, having good experience in solving polynomial equations is so interesting and important in linear algebra.
A lot of students don’t give that importance until they realize that in the late times, facing a linear algebra course.
which is so interesting for the next part will be talking about
5 – systems
The last thing that makes students face linear algebra is having a weak basis in systems. For instance, many linear algebra courses can t solve simple styles like this one example below:
When it comes to solving a group of problems like matrices. many students are unable to deal with matrices columns and rows because they are bad and still struggling with systems as we mentioned in the previous simple examples.
6 – having bad professors
The terrible thing is that you don’t have control or have to blame yourself is falling behind a bad professor. having a bad professor in such a complex topic as linear algebra can shake your confidence in yourself.
If you have this problem and looking for alternatives, you can be looking for other alternatives to learn linear algebra such as Khan Academy online courses, or ask for help from other people knowledgeable in math.
7 – study it the wrong way
The last problem that makes a group of students struggle in linear algebra is studying it in the wrong way means these two cases:
linear algebra is a topic that requires a lot of hard work and time to absorb, to complete this course we recommend devoting at least 2 to 3 hours a day for 3 months.
the second thing is to make sure that you understand lectures well before you go to the application or solve problems. This is a mistake a lot of students make. They go and rush directly to solve problems then find difficulties in problems and stuck on.
so take your time and make sure you understand every tiny element of the lecture before you move ahead.