Math Is Fun Forum

Migael

Member

Registered: 2016-12-25

Posts: 5

Linear Algebra

Hello everyone,

My question is about linear algebra. I am curious to know why or how linear equations, matrix equations and vector equations are connected. You can write them all three in their own unique form and solve for them, but why three of them what is the point? What is behind it?

I figured out myself that a linear combination a sum of the vector equations is. Yet I am still struggling to understand the different apporaches in linear algebra. Also I know that a linear transformation is from the basis i- and j-hat multiplied by a matrix. So a matrix 2x2 means that i-hat is the first column and j-hat is the second column.

Thank you in advance.

Last edited by Migael (2016-12-25 03:10:01)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear Algebra

Hi;

Welcome to the forum. Everything in math is connected. Do you have a specific question?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Migael

Member

Registered: 2016-12-25

Posts: 5

Re: Linear Algebra

Hello, thanks for the welcome.

Yes my question is:

You have linear equations, vector equations and matrix equations. The vector equations can be combined to linear combinations and that can be transformed into something else. However I don't understand why you can write linear equations as a matrix, vector also. Why are so many names and definitions used to describe basically the same thing? I am not able to discern between the importance of them all.

It is like I am learning a lot of new definitions that are all in the same course (linear algebra) but I do not see the point of the new meanings, cause basically I can do the assignments with just vector equations. 

So why all the definitions if we can make due with just vector equations?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear Algebra

Hmmm, I tend to agree with you and an answer I do not have. All I can say is that there are lots of ways to do the same thing in mathematics. For one thing while you obviously use vectors alot, I never use them! I use linear algebra for almost all problem solving whenever I can. But matrices are really just a bunch of vectors and some programming languages like mathematica think of them like that. To say I am not much of a theoretician is an understatement, I say use what you like.

So why all the definitions if we can make due with just vector equations?

That I do not agree with. Sooner or later you will run into a problem that will respond much better when you abandon a vector approach and look at it in another framework, another way. It pays to be able to view math from different angles, from different viewpoints. Matrices are an incredibly versatile tool and it is not hard to believe that lots of math can be expressed and done using them. That is about the most general I can get.

Here is a viewpoint I use because it works, learn it now while you can. Understanding and thus a use for it will come later and then it will all be clear to you.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.