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Author Topic: Who understands the matrix equation Ax=b?  (Read 4983 times)

jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #50 on: 17/01/2016 22:17:46 »
The answer to both questions is enough to get into trouble but not enough to get out. I certainly understand the basic posits and incidentally most of the disagreements. That's why I need a physicist.

I think you need to target your learning. The problem can be that to learn a subject you need it is often necessary to learn other basic elements. What you have to avoid is picking up too much material that isn't pertinent. It can confuse the issues and just slows you down. You aren't studying for a Phd so that frees you up somewhat. Let me know what areas you feel you need to learn and I may be able to recommend some texts. If not I can ask around to see what you might be better off reading. Getting the right text is crucial.

Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #51 on: 17/01/2016 22:20:08 »
The solution to the problem is

x = -13.145
y =  7.495
z = -9.205

Go here http://www.bluebit.gr/matrix-calculator/

Type the following with spaces into the matrix text area and click matrix inverse and then calculate

2    1   -4
4    5   -1
0    3    3

You should then get a new matrix with the values:

-0.750  0.625 -0.792
0.500 -0.250  0.583
-0.500  0.250 -0.250

Copy this then click on back to online matrix calculator and then click the link matrix multiplication.

Copy the results matrix into the matrix a box then type the following into the matrix b box

3
-6
50

Then click multiply A*B. You will then get the solution for x, y and z.

Using a calculator is cheating and I still have no idea of what it is trying to show or represent?

We started out with 3 equations

2x + y - 4z = 3
4x + 5y - z = -6
3y - 3z = 50

The solution is the values for x, y and z that solved ALL 3 equations.

Using the calculator was a way to show, via an online tool, what the correct answer was.

x = -13.145
y =  7.495
z = -9.205

So the equations now become

2 * -13.145 + 7.495 - 4 * -9.205 = 3
4 * -13.145 + 5 * 7.495 - -9.205 = -6
3 * 7.495 - 3 * -9.205 = 50

I don't know how much more straightforward I can make it.

I understand where to put the values you gave, but that is not answering my question, what are you equating?

2 * -13.145 + 7.495 - 4 * -9.205 = 3   i.e  3 apples, 3 jules, 3 newtons,

jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #52 on: 17/01/2016 22:39:50 »
In this case x, y and z are just numbers with no specific meaning. This is just an example of the process. What matters is that you can solve a set of equations. These could be energy equations where kinetic energy is subtracted from potential energy, or momentum equations. That is up to you to decide. As long as the equations form a sum such as x + y - z.

Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #53 on: 17/01/2016 22:51:34 »
In this case x, y and z are just numbers with no specific meaning. This is just an example of the process. What matters is that you can solve a set of equations. These could be energy equations where kinetic energy is subtracted from potential energy, or momentum equations. That is up to you to decide. As long as the equations form a sum such as x + y - z.

Ok, I think I see what you are saying.   I suppose it is dependent to the equation and the persons interests,  if a person is more interested in the physical process rather than the maths representing a physical process, I personally do not think this should hamper a wanting to be scientist.  The thought process always comes first before the maths. Without the thought there is no maths.
Like myself I do not know this maths, I know some other maths such as F=ma which I wanted to learn. I can even create maths , banned on here from posting maths any more for some reason.
I can not think where anywhere in my life would have a need to know your equation.

evan_au

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Re: Who understands the matrix equation Ax=b?
« Reply #54 on: 19/01/2016 17:33:03 »
Quote from: TheBox
I can not think where anywhere in my life would have a need to know your equation.
Have you ever played a 3D computer game? Or watched just about any film made in the past 20 years? Or used a cellphone, or a WiFi hotspot?

Modern computer graphics makes extensive use of matrices of x, y, z points to represent the shape of every object on the screen. Every time you move in the game, or the camera pans in the film, the GPU does millions (or billions) of matrix operations to transform the location of each point in the scene to its new location on the screen.

Modern wireless telecommunications makes use of multiple antennas in your cellphone, computer, WiFi hotspot and mobile base station. To work out what is the best way to transfer data over these multiple possible paths requires "channel state estimation", which involves solving matrix equations such as those described by Jeffrey.

If you are moving while talking or browsing or using social media (or other people around you are moving), these matrix equations must be solved many times per second to maximize the quantity of data transferred, and minimize delays.

Quote
I know some other maths such as F=ma which I wanted to learn.
Single numbers like m in the above equation are called "scalars", and they obey the arithmetic we were taught in primary school and high school.

In junior high-school physics, F and a were also represented as scalars, which is fine if the force and acceleration are all in a straight line. But real forces don't operate in a straight line - think of the forces on billiard balls, which move in a 2 dimensional space, or a planet which moves in a 2D elliptical orbit around its star.

Real cars, planes, spaceships, buildings and bridges operate in a 3 dimensional world, where forces can come from any direction, so scalars are not sufficient for real applications. In these applications, F and a are represented as vectors, and their interactions are represented as matrices.

Matrix arithmetic is an extension of high-school scalars, but "grown up" to work in the real world. I was taught this at university level, but given the ease of calculating with them using computers, I don't see why they couldn't be introduced earlier, these days.

Every time you drive your car over a bridge, or catch a plane, be grateful that someone was able to apply F=ma using matrices.

The following users thanked this post: jeffreyH, Thebox

Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #55 on: 19/01/2016 17:52:38 »
Quote from: TheBox
I can not think where anywhere in my life would have a need to know your equation.
Have you ever played a 3D computer game? Or watched just about any film made in the past 20 years? Or used a cellphone, or a WiFi hotspot?

Modern computer graphics makes extensive use of matrices of x, y, z points to represent the shape of every object on the screen. Every time you move in the game, or the camera pans in the film, the GPU does millions (or billions) of matrix operations to transform the location of each point in the scene to its new location on the screen.

Modern wireless telecommunications makes use of multiple antennas in your cellphone, computer, WiFi hotspot and mobile base station. To work out what is the best way to transfer data over these multiple possible paths requires "channel state estimation", which involves solving matrix equations such as those described by Jeffrey.

If you are moving while talking or browsing or using social media (or other people around you are moving), these matrix equations must be solved many times per second to maximize the quantity of data transferred, and minimize delays.

Quote
I know some other maths such as F=ma which I wanted to learn.
Single numbers like m in the above equation are called "scalars", and they obey the arithmetic we were taught in primary school and high school.

In junior high-school physics, F and a were also represented as scalars, which is fine if the force and acceleration are all in a straight line. But real forces don't operate in a straight line - think of the forces on billiard balls, which move in a 2 dimensional space, or a planet which moves in a 2D elliptical orbit around its star.

Real cars, planes, spaceships, buildings and bridges operate in a 3 dimensional world, where forces can come from any direction, so scalars are not sufficient for real applications. In these applications, F and a are represented as vectors, and their interactions are represented as matrices.

Matrix arithmetic is an extension of high-school scalars, but "grown up" to work in the real world. I was taught this at university level, but given the ease of calculating with them using computers, I don't see why they couldn't be introduced earlier, these days.

Every time you drive your car over a bridge, or catch a plane, be grateful that someone was able to apply F=ma using matrices.

arrgg right, thank you for explaining . I use CGI software and this uses this,I now recognise the use .

dhjdhj

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Re: Who understands the matrix equation Ax=b?
« Reply #56 on: 19/01/2016 18:47:21 »
Evan you are spot on in both your explanation and suggestion. I learnt in the sixth form, but I think basic matrix algebra could easily be introduced much earlier. My grand daughter is learning to code at eight years old, and her understanding of mathematical logic is frightening.

Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #57 on: 19/01/2016 18:54:24 »
Evan you are spot on in both your explanation and suggestion. I learnt in the sixth form, but I think basic matrix algebra could easily be introduced much earlier. My grand daughter is learning to code at eight years old, and her understanding of mathematical logic is frightening.

The thing is with using calculators you are not teaching anyone maths in my opinion, you are teaching them mimic to use a calculator.

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Re: Who understands the matrix equation Ax=b?
« Reply #57 on: 19/01/2016 18:54:24 »