Matrix over Z7 needs revision please

  • Thread starter Thread starter JPanthon
  • Start date Start date
  • Tags Tags
    Matrix Revision
Click For Summary
SUMMARY

The discussion focuses on solving a system of linear equations over the finite field Z7, specifically the equations -x1 + 6x2 - 2x3 = 0 and 5x1 + x2 + 2x3 = 0. The solution set is expressed as {(-4x3, -x3, x3) : x3 ∈ Z7}, indicating multiple solutions exist due to the presence of a free variable, x3. Additionally, participants discuss formatting matrices using LaTeX for clearer presentation, referencing a specific post (#3) for guidance on LaTeX syntax.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically systems of equations.
  • Familiarity with finite fields, particularly Z7.
  • Basic knowledge of matrix operations and row reduction techniques.
  • Proficiency in LaTeX for mathematical typesetting.
NEXT STEPS
  • Study the properties of finite fields, focusing on Z7 and its applications in linear algebra.
  • Learn matrix row reduction techniques to solve systems of equations efficiently.
  • Explore LaTeX documentation to improve mathematical formatting skills.
  • Investigate the implications of free variables in linear systems and their solution sets.
USEFUL FOR

Students of linear algebra, mathematicians working with finite fields, and anyone interested in improving their LaTeX formatting skills for mathematical expressions.

JPanthon
Messages
20
Reaction score
0

Homework Statement



Solve

-x1 + 6x2 -2x3 = 0
5x1 + x2 + 2x3 = 0

over Z7

Additional Question: How can we immediately tell there is more than one solution?

Homework Equations

Don't know.

The Attempt at a Solution



[-1 6 -2 0]_________[ (-1mod7) 6 (-2mod7) 0]
[5 1 2 0] _____=> [____5_____1____2_____0]=> [1 6 2 0] (-5R1 + R2) => [1_____6__________2_____0]
____[5 1 2 0] ________________[0___-29mod7___-8mod7___0]

=> [1 6 2 0]________(-6R2 + R1) => [1 0 4 0]
____[0 1 1 0]______________________[0 1 1 0]
So the solution set is {(-4x3, -x3, x3) : x3 element of Z7}How does this look?
Sorry if it's messy! I did my best
 
Physics news on Phys.org
Just realized how ugly it looks!
Sorry, just ignore the underscores and pretend that they are spaces.
Or if you could tell me how to make better matrices on the computer I would be happy to redo my post!
 
JPanthon said:
Just realized how ugly it looks!
Sorry, just ignore the underscores and pretend that they are spaces.
Or if you could tell me how to make better matrices on the computer I would be happy to redo my post!

Post #3 in this LaTeX thread shows a matrix. You can use the "Quote" button on it to see the LaTeX source that was used to make it.
 

Similar threads

Is there a better way to find the number of integer solutions
  • · Replies 5 ·
Replies
5
Views
3K
Spectral decomposition of 4x4 matrix
  • · Replies 2 ·
Replies
2
Views
2K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
  • · Replies 2 ·
Replies
2
Views
2K
Solving a separable matrix ODE.
  • · Replies 3 ·
Replies
3
Views
2K
Linear Transformation (Image, Kernel, Basis, Dimension)
  • · Replies 24 ·
Replies
24
Views
3K
Does it matter in which order I assign the values?
  • · Replies 11 ·
Replies
11
Views
2K
Find the basis of a vector subspace of R^2,2
  • · Replies 9 ·
Replies
9
Views
4K
Matrix Relative to B and B' R3 to R3
  • · Replies 1 ·
Replies
1
Views
2K
Finding a matrix W such that W^t*AW = D (D is diagonal matrix)
  • · Replies 3 ·
Replies
3
Views
2K
S, T and U are all subspaces of R4. Subspace & Subset Homework in R4
  • · Replies 10 ·
Replies
10
Views
3K