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rwells1-Visitor
1-Visitor
January 4, 2013
Solved

Linear Algebra programming

  • January 4, 2013
  • 4 replies
  • 11425 views

For linear algebra most students find it very difficult to "visualize" three or more variables. It is so much easier to understand the solution set and linear dependence on a simple xy coordinate plane. For three variables, most college algebra books include pictures and graphs of lines and planes in 3d space. I have found it very difficult to make a graph of lines in 3d space on mathcad. They are asking for constraints and I can not simply define an function of three ordered pairs and point and click my way to a graph. The only example that even comes close (in the mathcad rescource center) is a graph of a helix. That is far to difficult for me. Can any one show an example of three lines in an xyz 3d plot?

Best answer by Werner_E

roger wells schrieb:

Valery and Werner . . .thankyou for these examples. I see now that I have considered a function like f(x) to be the same as f(x,y) when in fact one is a curve and the other is a surface (or plane). If I want lines then I am going to need to do some review of vectors and the calculus of space geometry.

That sure would help 😉

A straight line in 3D can either be described by a parametric representation (like the helix, you mentioned) or via a system of two linear equations in x,y and z (that is a the intersection of two planes).

In the attached file I've tried to make it easier to deal with points, line segments and straight lines in Mathcads 3D graph. 3D graph is able to plot points and you may chose that you want it to connct it with lines. This is what my function "Strecke" does - you call it with two vectors (representing the two endpoints of the line segment) as parameters and it returns an expression which you can put in the placeholder of a 3D-graph and you should see a line segment. Unfortunately you will have to format the graph (data point, check chekbox lines, otherwise you will only see the two small points). In the attached file I have added a function for a "real" infinite straight line. This has to be formated as surface plot, not Data points.

But to be honest, Mathcads 3D functionality is not really top notch for your purpose.

I have saved the file in Mathcad 11 format, but I doubt that your Mathcad 2000 will be able to read it.

If you think that a screenshot of the functions or a pdf printout will help, give me a shout.

4 replies

R
RogerYeh1-Visitor
1-Visitor
January 4, 2013

Put the points you want into a matrix with three columns (for x, y, and z points). Plot it on a 3D plot. By default, you will get points. If you want a line, under the Plots tab, pick Styles, choose your Line Style to include a line. Default will be (none). Is this what you mean?

Untitled.png

R
rwells1-VisitorAuthor
1-Visitor
January 4, 2013

Thankyou, I am on a library computer so will have to go home and investigate this.

J
jkowalski1-Visitor
1-Visitor
January 4, 2013

a few examples....

R
rwells1-VisitorAuthor
1-Visitor
January 5, 2013

Jan thankyou but I am not able to open a mcd document on library computers. I only have mathcad professional 2000 and no internet, which pretty much sucks.

V
VladimirN24-Ruby III
24-Ruby III
January 5, 2013

I converted this files to Mathcad 2000 version. Please see attachment.

V
ValeryOchkov24-Ruby IV
24-Ruby IV
January 5, 2013

One Mathcad illustration of the main linear algebra theorem (from Wikipedia).

Rouché–Capelli theorem is the theorem in linear algebra that allows computing the number of solutions in a system of linear equations given the ranks of its augmented matrix and coefficient matrix. The theorem is known as Kronecker–Capelli theorem in Russia, Rouché–Capelli theorem in Italy, Rouché–Fontené theorem in France and Rouché–Frobenius theorem in Spain and many countries in Latin America.

A system of linear equations with n variables has a solution if and only if the rank of its coefficient matrix A is equal to the rank of its augmented matrix [A|b]. If there are solutions, they form an affine subspace of \mathbb{R}^n of dimension n − rank(A). In particular:

  • if n = rank(A), the solution is unique,
  • otherwise there are infinite number of solutions.

3-Lin-Plot-Eng.png

R
rwells1-VisitorAuthor
1-Visitor
January 5, 2013

Valery and Werner . . .thankyou for these examples. I see now that I have considered a function like f(x) to be the same as f(x,y) when in fact one is a curve and the other is a surface (or plane). If I want lines then I am going to need to do some review of vectors and the calculus of space geometry.

W
Werner_E25-Diamond IAnswer
25-Diamond I
January 5, 2013

roger wells schrieb:

Valery and Werner . . .thankyou for these examples. I see now that I have considered a function like f(x) to be the same as f(x,y) when in fact one is a curve and the other is a surface (or plane). If I want lines then I am going to need to do some review of vectors and the calculus of space geometry.

That sure would help 😉

A straight line in 3D can either be described by a parametric representation (like the helix, you mentioned) or via a system of two linear equations in x,y and z (that is a the intersection of two planes).

In the attached file I've tried to make it easier to deal with points, line segments and straight lines in Mathcads 3D graph. 3D graph is able to plot points and you may chose that you want it to connct it with lines. This is what my function "Strecke" does - you call it with two vectors (representing the two endpoints of the line segment) as parameters and it returns an expression which you can put in the placeholder of a 3D-graph and you should see a line segment. Unfortunately you will have to format the graph (data point, check chekbox lines, otherwise you will only see the two small points). In the attached file I have added a function for a "real" infinite straight line. This has to be formated as surface plot, not Data points.

But to be honest, Mathcads 3D functionality is not really top notch for your purpose.

I have saved the file in Mathcad 11 format, but I doubt that your Mathcad 2000 will be able to read it.

If you think that a screenshot of the functions or a pdf printout will help, give me a shout.

W
Werner_E25-Diamond I
25-Diamond I
January 5, 2013

Valery has shown how to graph planes, but as you asked for lines in 3D space i thought the attached would help.

Unfortunately the formatting (checkbox "lines" is not activated on default, etc.) cannot be done parameter driven but has to done manually.

You did not specify if you are interested in Mathcad15 or Mathcad Prime. The attched information is for Mathcad 15.

3D-Alg1.png

J
jkowalski1-Visitor
1-Visitor
January 5, 2013

H264 encoding animations give better results and a video file is 16 times less.With the same quality.Upload is very fast.

V
ValeryOchkov24-Ruby IV
24-Ruby IV
January 5, 2013

Better to use PlanetPTC Video for animation - http://communities.ptc.com/community/mathcad?view=video

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