## What did I wrong: Determine the complete solution ...

I tried to solve this problem.

It is a Maple TA question, but I get my solution wrong.

***********************

Question:

There is given a linear equation system consisting of two equations with four unknowns.

## Extract a factor...

I would like to express a matrix in a neat(er) form.  For example, both matrices;

Matrix([[1/4, 1/2], [1/2, 1/4]]);

(1/2)*Matrix([[1/2, 1],[1, 1/2]]);

return the same thing.  I would like maple to print the latter with the factor 1/2 preceding the matrix for better clarity.  Is there a simple command that will do this?

Rob

## Find an invertible matrix P...

How do I find find an invertible matrix P and the diagonal matrix D such that A=PDP. Are there a Maple command that can do that. I need it to an Maple T.A. exam.

A=

(−3 0 6)
(0 -3 −6)
(0 0 3)

## Define values for matrix elements?...

Hello

I have a matrix consisting of 4 variables. I want to define the values of these. Example:

A:=Matrix(2,2,[a,b,c,d]);

I am looking for an easy way to put a=0, b=0, c=0 and d=0. If I just use

A:=Matrix(2,2,0);

the variables are replaced by zeros, and not assigned zeroes as values. I know I can do it manually (by a:=0 etc.). Is there an easier way?

## Matrix operations - extract element equations?...

Hello

I want to create three matrices, multiply two of them, equate the result to the third, and extract the individual matrix element equations:

A:=Matrix(2,2,[1,2,3,4]);

B:=Matrix(2,2,[2,3,4,5]);

C:=Matrix(2,2,[a,b,c,d]);

## Calculations With Matrix in Matrix...

I try to make calculation with matrix in matix for example

n1 >0 , n2 >0; n1 ,n2 unknow
matirx  A11 := matrix(n1,n1,[unknow variables ]);
matirx  A12 := matrix(n1,n2,[unknow variables ]);
matirx  A21 := matrix(n2,n1,[unknow variables ]);
matirx  A22 := matrix(n2,n2,[unknow variables ]);

A_big := matrix(n1+n2,n1+n2 , [[A11,A12],[A21,A22]]);

how i will sovle

A_big ^ (-1) ;

matrix(...

## LinearAlgebra(Matrix)...

Hi
first : My English not good,so excuse me.
I have a problem with this:

1)C+Z*(C)*X=D where;

I know D , Z and X are matrix(n*n),(known)
but i can`t find C or Solve (1)finding C(matrix(n*n))

Help Me

Reza

## solving system of equations using matrix...

Dear Sir

I want to solve system of algebric equations using matrix

can you help me to do that

> restart;

> Digits:=6:

> s:=140:

## creating Eigenvalues with 14x14 matrix...

Hello.

I have a problem with creating eigenvalues of a 14x14 matrix.

when i execute "LinearAlgebra[Eigenvalues](A)" there are only results like "-3.2211+29.1111I"

The problem is the 'I' at the end. I need numeric values for plotting or stuff like that.

Wheres my mistake? I have no clue.

Im looking forward to any suggestions! At the bottom...

## creating a matrix out of matrices...

Hi!

I have a serious problem and im looking forward to any suggestions.

Like i already wrote i wanna create a simple matrix (14x14) out of four matrices(7x7) and i have no clue how to accomplish this task in maple.

to be more specific, i want to create matrix M=(A,B,C,D) each of them is another 7x7 which results in a 14x14 matrix.

I guess its a simple task but i tried hard and didnt get it worked.

thank you  in anticipation

## Solving Dense Linear Systems in Maple 12

by: Maple 12

Suppose you want to solve a large dense linear system AX=B over the rationals - what should you do? Well, one thing you should probably not do is directly apply Gaussian elimination. It does O(n^3) arithmetic operations, but the size of the numbers blow up, leading to an exponential bit complexity. Don't believe me? Try it:

```with(LinearAlgebra):
for N from 5 to 9 do
A := RandomMatrix(2^N, 2^N+1,generator=-10^5..10^5):
TIMER := time(GaussianElimination(A...```

## Building Up Sets and Removing Redundant Elements

by: Maple

"I've seen this element before..." Often we are faced with the problem of building up sets incrementally, by removing pieces one at a time from a larger whole. The bottlenecks in this case are usually: 1) adding a small set X to a large set S (copies S and X, making this ~O(|S|+|X|)) 2) removing elements of the large set S from the small set X (binary search: |X|*log(|S|)) A classic example of this is a breadth-first-search. We start at one vertex of a graph and in each iteration we add the set of new neighbors X to the set of vertices S that have already been found. We can make this more useful by making the program return the sets of new neighbors found in each iteration, that is, the sets of vertices that are distance 1, 2, 3, etc. from the initial vertex.

## Plotting Large Sparse Matrices in Maple

by: Maple

When working with large sparse linear systems you often want to look at their non-zero structure, however Maple's existing tools are all designed for dense matrices. I wrote a little tool to produce images like this in reasonable time. You can download the code here, and the rest of this post is a quick tutorial on how to use the included command. Maple 11 is required.

## Solving Sparse Linear Systems in Maple

by: Maple

What is the largest linear system that Maple can solve? You might be surprised to find out. In this article we present strategies for solving sparse linear systems over the rationals. An example implementation is provided, but first we present a bit of background. Sparse linear systems arise naturally from problems in mathematics, science, and engineering. Typically many quantities are related, but because of an underlying structure only a small subset of the elements appear in most equations. Consider networks, finite element models, structural analysis problems, and linear programming problems.

## Sparse Matrix-Vector product using evaluation

by: Maple

This tip comes care of Dr. Michael Monagan at Simon Fraser University. Represent your sparse matrix as a list of rows, and represent each row as a linear equation in an indexed name. For example:

A := [[1,0,3],[2,0,0],[0,4,5]];

S := [ 1*x[1] + 3*x[3], 2*x[1], 4*x[2]+5*x[3] ];

To compute the product of the matrix A with a Vector X, assign x[i] := V[i] and evaluate. This can be done inside of a procedure because x is a table.

V := [7,8,9]: for i to 3 do x[i...

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