Linked Questions

6
votes
4answers
3k views

how to find inverse of a matrix in $\Bbb Z_5$

how to find inverse of a matrix in $\Bbb Z_5$ please help me explicitly how to find the inverse of matrix below, what I was thinking that to find inverses separately of the each term in $\Bbb Z_5$ and ...
3
votes
1answer
6k views

How to find Matrix Inverse over finite field?

How to find matrix Inverse over finite field? I am using MATLAB, and I know gf() in MATLAB can enable me to do linear algebra operations over finite field $F_{2^m}$ for some m. However, if I want to ...
1
vote
1answer
2k views

How do you solve a system of linear equations in modular arithmetic.

I'm finding a hard time trying to proceed with this cryptography problem: If i'm given such a system of linear equations: $3x+5y+7z\equiv3 (mod\ 16)$ $x+4y+13z\equiv5 (mod\ 16)$ $2x+7y+3z\equiv4 (...
0
votes
1answer
1k views

Who to solve this linear modular equation system?

I have this equation system: a + b + c (mod 11) = 8 9a + 3b + c (mod 11) = 2 16a + 4b + c (mod 11) = 9 Unfortunately I totally don't know how to solve it. It is in general part of Lagrange's ...
2
votes
2answers
169 views

System of equation over GF(211) (corrected)

I have this system of equation. $a+b+c=171, a+2b+4c = 46, a+3b+9c = 170$. My task is to solve this system over $GF(211)$. Is there any special process? Thanks for advice.
1
vote
1answer
490 views

How to compute inverse of a matrix over finite field?

My guess is : Given $A$ a square matrix, then $A^{-1}=det(A)^{-1}adj(A)$ where $det(A)^{-1}$ is multiplication inverse of $det(A)$
5
votes
1answer
362 views

calculating with residue classes in $\mathbb{Z}{/5\mathbb{Z}}$

How to calculate with residue classes in $\mathbb{Z}{/5\mathbb{Z}}$? $- \overline x \neq \overline x$ but $- \overline x = \overline{5-x}$ $\overline x + \overline y = \overline{x+y}$ $\overline x \...
2
votes
0answers
529 views

Finite fields: Compute the inverse of a matrix

I am working with finite fields in Python. I have a matrix containing polynomials, each polynomial is represented as an integer. For example, the polynomial ...
1
vote
0answers
376 views

solving congruence equation system modulo prime

I need to solve a congruence system like this: $30f_0+26f_1+8f_2+38f_3+2f_4+40f_5+20f_6 \equiv 0 \pmod{41}$ $38f_0+2f_1+40f_2+20f_3+30f_4+26f_5+8f_6 \equiv 0 \pmod{41}$ $40f_0+20f_1+30f_2+26f_3+8f_4+...
1
vote
3answers
74 views

Any difference working with matrices over fields?

Is there any difference regarding row operations and such with matrices when they are over fields? For instance, I have the following matrix over GF(3): ...
0
votes
1answer
206 views

Matrix inverses over finite fields with composite moduli

I know that over a field $F$, a matrix is invertible if and only if its determinant is nonzero. And I understand why this is true, at least in the case where the field is $\mathbb{R}$. But I do not ...
0
votes
4answers
67 views

Is this method to solve a system of equations in modular arithmetic correct?

We seek to solve the sytem of equations: $\left\{ \begin{array}{cc} \bar 3x + \bar2y &= \bar1 \\ \bar 5x + \bar1y &= \bar4 \end{array} \right.$ In $\mathbb{Z}_{19}$ The following ...
2
votes
0answers
204 views

Efficient computation of matrix determinant in finite ring

I am trying to implement generalization of Hill cipher. My idea is very simple: the size of key matrix should be arbitrary number not only three. All steps of this cipher is trivial except computation ...
0
votes
0answers
200 views

Find A^−1 modulo 26.

Find A^−1 modulo 26. |4 9 15 | |15 17 6| |24 0 17| i know i will have to do something like this |4 9 15 | * | 1 0 0 | |15 17 6| * | 0 1 0 | |24 0 17| * | 0 0 1 | Also if the product of the ...
2
votes
1answer
154 views

How to find the inverse of the matrix over $\mathbb Z_5$

How to find the inverse of the matrix over $\mathbb Z_5$ $$ \left( \begin{matrix} 1 & 2& 0\\ 0 &2& 4 \\ 0& 0& 3\\ \end {matrix} \right) $$

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