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Is there a way to do the following on Maple:

I want Maple to use Jacobi's method to give an approximation of the solution to the following linear system, with a tolerance of 10^(-2) and with a maximum iteration count of 300.

 

The linear system is

x_1-2x_3=0.2

-0.5x_1+x_2-0.25x_3=-1.425

x_1-0.5x_2+x_3=2

 

Thanks.

Exercise Prove that (-1)u = - u in any vector space. Note that (-1)u means the number -1 is multiplied to the vector u, and - u means the negative vector in the fourth property of the definition of vector spaces.

Answer

Exercise Prove that (a1u1 + a2u2) + (b1u1 + b2u2) = (a1 + b1)u1 + (a2 + b2)u2 in any vector space.

Answer

Exercise Give a detailed reason why, in any vector space,

  • u + v = 0 ⇒ u = - v.

  • 3u + 2v - 4w = 0 ⇒ v = - 3/2 u + 2w.

I wrote down a proceduer in maple for solving integro diff. equations which result in an ill conditioned linear system of algebraic equations. I used the LinearSolve command with method=LU to solve the system but my algorithm failed, and does not converge. Is there any command in maple for solving such systems

let A be a matrix=

 

[  7        7      9    -17

   6        6      1    -2

 -12    -12    -27    1

   7       7      17   -15 ]

What is the reduced row echelon form of A?

What is the rank of A?

A consistent system of linear equations in 14 unknowns is reduced to row echelon form. There are then 10 non-zero rows (i.e. 10 pivots). How many parameters (free variables) will occur in the solution?

hi fellas
i have questions which maybe very common but i can't handle it right now
there are 9 matrices. each one of them is a 3*3 matrix, not to say all the matrices' elements are in symbolic form.
all i want is to form a matrix made out of the 9 matrices i mentioned above in **maple**; i mean something like "cell" in MatlabI'll be appreciated for your help

 http://en.wikibooks.org/wiki/Linear_Algebra/

Representing_Linear_Maps_with_Matrices

 

how to calculate the first step

(2,0) -> (1,1,1) and (1,4) -> (1,2,0)

how to use maple command to get (1,1,1) and (1,2,0)

how to use maple command to calculate rep(h)

 

to get (0,-1/2,1) and (1,-1,0)

http://en.wikibooks.org/wiki/Linear_Algebra

/Representing_Linear_Maps_with_Matrices

So im trying to write a maple script that computes the Jordan form of a given (3x3)- matrix
A. If {a,b,c} is a basis with respect to which A is in Jordan form, then I'm trying to make it
plot the three lines spanned by a, b and c, in the standard coordinate system. I was hinted to use plot3d here.

sidenote: I know how to compute the jordan matrix of A, such by find the eigen vectors and generalised eigen vectors and putting them in as columns in a 3x3 matrix say S,   where S is invertible    then  (S^-1)*(A)*(S) = (J).

Thanks in advance. <3

In my research a I need to solve the linear equation (getting its null space) under some constraints.

The matrix is given below:

 

The constraints shall be (x[1]...x[16]>0, x[17]...x[20] arbitary...)

The solutions shall actually be a canonical combination of a lot of vectors, (canonical combination means possitive sums of vectors). And I wish to get those vectors. is there a way that I could achieve this by Maple?

how can i convert these equations to the vector mode ? 

eq1[t] := .4614468816e11*a[13][t]*a[14][t]+2291210.983*a[16][t]^2-.2842690977e11*a[17][t]^2-.1782456232e12*a[18][t]^2+.1689228391e12*a[13][t]^2+6406045.412*a[14][t]^2-4317791.317*a[15][t]^2+.9846526429e12*a[1][t]+.2533881291e12*a[2][t]+.3076607771e11*a[3][t]+8105875.203*a[4][t]-5054889.363*a[5][t]-34561.30764*a[6][t]-6275707.162*a[16][t]*a[13][t]-20873274.82*a[14][t]*a[16][t]-27435155.86*a[16][t]*a[15][t]-5539558.102*a[17...

Think of ranking as a vector in R^Z, where Z is the total number of webpages on the web.

For a given network of Z web pages, let A = [a_jk(little)] be the matrix

a_jk(little) = { 1 if page k has a link to page j

                  { 0 otherwise

1. How do you determine the matrix A for my network of pages?

2. And the number of recommendations that page j gets...

 

Hi,

I have this system of lienar equations:

I need to write a procedure to check whether a group of input vectors is an orthonormal basis. If anyone can help me with this I would really appreciate it. Thanks.

If S= { <0,1>,<1,2>} and T={<1,1>,<2,3>} are ordered bases for R2 and v=<1,5> and w=<5,4>, then can someone help me:

-find the coordinate vector of v and w with respect to the basis T by creating a procedure?

-I can make a procedure to find the transition matrix PS<-T from T to S-basis, but can you help find the coordinate vector of v and w with respect to the basis S. Using PS<-T?

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